Find the Determinant [[4,-3,5,2,4],[1,6,3,-5,-3],[7,3,-4,-4,-5],[2,-1,8,-6,7],[6,3,-5,5,-2]]

$[\begin{array}{c} 4 & - 3 & 5 & 2 & 4 \\ 1 & 6 & 3 & - 5 & - 3 \\ 7 & 3 & - 4 & - 4 & - 5 \\ 2 & - 1 & 8 & - 6 & 7 \\ 6 & 3 & - 5 & 5 & - 2 \end{array}]$

Set up the determinant by breaking it into smaller components.

$4 | \begin{array}{c} 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$4 (6 | \begin{array}{c} - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $6 | \begin{array}{c} - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$4 (6 (- 4 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} | - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 4 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (6 (- 4 ((- 6) (- 2) - 5 \cdot 7) - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 6$ by $- 2$ .

$4 (6 (- 4 (12 - 5 \cdot 7) - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $7$ .

$4 (6 (- 4 (12 - 35) - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $35$ from $12$ .

$4 (6 (- 4 \cdot - 23 - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 4$ by $- 23$ .

$4 (6 (92 - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (6 (92 - 8 ((- 4) (- 2) - 5 \cdot - 5) - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $- 2$ .

$4 (6 (92 - 8 (8 - 5 \cdot - 5) - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 5$ .

$4 (6 (92 - 8 (8 + 25) - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $8$ and $25$ .

$4 (6 (92 - 8 \cdot 33 - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 8$ by $33$ .

$4 (6 (92 - 264 - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (6 (92 - 264 - 5 ((- 4) (7) + 6 \cdot - 5)) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $7$ .

$4 (6 (92 - 264 - 5 (- 28 + 6 \cdot - 5)) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 5$ .

$4 (6 (92 - 264 - 5 (- 28 - 30)) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $30$ from $- 28$ .

$4 (6 (92 - 264 - 5 \cdot - 58) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 58$ .

$4 (6 (92 - 264 + 290) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $264$ from $92$ .

$4 (6 (- 172 + 290) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 172$ and $290$ .

$4 (6 (118) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $118$ .

$4 (708 - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$4 (708 - 3 (3 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} | - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $3 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 - 3 (3 ((- 6) (- 2) - 5 \cdot 7) - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 6$ by $- 2$ .

$4 (708 - 3 (3 (12 - 5 \cdot 7) - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $7$ .

$4 (708 - 3 (3 (12 - 35) - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $35$ from $12$ .

$4 (708 - 3 (3 \cdot - 23 - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $3$ by $- 23$ .

$4 (708 - 3 (- 69 - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 - 3 (- 69 - 8 ((- 5) (- 2) - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 2$ .

$4 (708 - 3 (- 69 - 8 (10 - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 3$ .

$4 (708 - 3 (- 69 - 8 (10 + 15) - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $10$ and $15$ .

$4 (708 - 3 (- 69 - 8 \cdot 25 - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 8$ by $25$ .

$4 (708 - 3 (- 69 - 200 - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 - 3 (- 69 - 200 - 5 ((- 5) (7) + 6 \cdot - 3)) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $7$ .

$4 (708 - 3 (- 69 - 200 - 5 (- 35 + 6 \cdot - 3)) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 3$ .

$4 (708 - 3 (- 69 - 200 - 5 (- 35 - 18)) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $18$ from $- 35$ .

$4 (708 - 3 (- 69 - 200 - 5 \cdot - 53) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 53$ .

$4 (708 - 3 (- 69 - 200 + 265) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $200$ from $- 69$ .

$4 (708 - 3 (- 269 + 265) - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 269$ and $265$ .

$4 (708 - 3 \cdot - 4 - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 4$ .

$4 (708 + 12 - 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 1 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$4 (708 + 12 - 1 (3 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $3 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 + 12 - 1 (3 ((- 4) (- 2) - 5 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $- 2$ .

$4 (708 + 12 - 1 (3 (8 - 5 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 5$ .

$4 (708 + 12 - 1 (3 (8 + 25) + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $8$ and $25$ .

$4 (708 + 12 - 1 (3 \cdot 33 + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $3$ by $33$ .

$4 (708 + 12 - 1 (99 + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 + 12 - 1 (99 + 4 ((- 5) (- 2) - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 2$ .

$4 (708 + 12 - 1 (99 + 4 (10 - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 3$ .

$4 (708 + 12 - 1 (99 + 4 (10 + 15) - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $10$ and $15$ .

$4 (708 + 12 - 1 (99 + 4 \cdot 25 - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $25$ .

$4 (708 + 12 - 1 (99 + 100 - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 + 12 - 1 (99 + 100 - 5 ((- 5) (- 5) + 4 \cdot - 3)) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$4 (708 + 12 - 1 (99 + 100 - 5 (25 + 4 \cdot - 3)) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 3$ .

$4 (708 + 12 - 1 (99 + 100 - 5 (25 - 12)) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $12$ from $25$ .

$4 (708 + 12 - 1 (99 + 100 - 5 \cdot 13) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $13$ .

$4 (708 + 12 - 1 (99 + 100 - 65) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $99$ and $100$ .

$4 (708 + 12 - 1 (199 - 65) - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $65$ from $199$ .

$4 (708 + 12 - 1 \cdot 134 - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 1$ by $134$ .

$4 (708 + 12 - 134 - 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$4 (708 + 12 - 134 - 3 (3 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} | + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $3 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 + 12 - 134 - 3 (3 ((- 4) (7) + 6 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $7$ .

$4 (708 + 12 - 134 - 3 (3 (- 28 + 6 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 5$ .

$4 (708 + 12 - 134 - 3 (3 (- 28 - 30) + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $30$ from $- 28$ .

$4 (708 + 12 - 134 - 3 (3 \cdot - 58 + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $3$ by $- 58$ .

$4 (708 + 12 - 134 - 3 (- 174 + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 + 12 - 134 - 3 (- 174 + 4 ((- 5) (7) + 6 \cdot - 3) + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $7$ .

$4 (708 + 12 - 134 - 3 (- 174 + 4 (- 35 + 6 \cdot - 3) + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 3$ .

$4 (708 + 12 - 134 - 3 (- 174 + 4 (- 35 - 18) + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $18$ from $- 35$ .

$4 (708 + 12 - 134 - 3 (- 174 + 4 \cdot - 53 + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 53$ .

$4 (708 + 12 - 134 - 3 (- 174 - 212 + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$4 (708 + 12 - 134 - 3 (- 174 - 212 + 8 ((- 5) (- 5) + 4 \cdot - 3))) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$4 (708 + 12 - 134 - 3 (- 174 - 212 + 8 (25 + 4 \cdot - 3))) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 3$ .

$4 (708 + 12 - 134 - 3 (- 174 - 212 + 8 (25 - 12))) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $12$ from $25$ .

$4 (708 + 12 - 134 - 3 (- 174 - 212 + 8 \cdot 13)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $8$ by $13$ .

$4 (708 + 12 - 134 - 3 (- 174 - 212 + 104)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $212$ from $- 174$ .

$4 (708 + 12 - 134 - 3 (- 386 + 104)) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 386$ and $104$ .

$4 (708 + 12 - 134 - 3 \cdot - 282) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 282$ .

$4 (708 + 12 - 134 + 846) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $708$ and $12$ .

$4 (720 - 134 + 846) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $134$ from $720$ .

$4 (586 + 846) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $586$ and $846$ .

$4 (1432) - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $1432$ .

$5728 - 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 1 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 1 (- 3 | \begin{array}{c} - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 1 (- 3 (- 4 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} | - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 4 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 3 (- 4 ((- 6) (- 2) - 5 \cdot 7) - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 6$ by $- 2$ .

$5728 - 1 (- 3 (- 4 (12 - 5 \cdot 7) - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $7$ .

$5728 - 1 (- 3 (- 4 (12 - 35) - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $35$ from $12$ .

$5728 - 1 (- 3 (- 4 \cdot - 23 - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 4$ by $- 23$ .

$5728 - 1 (- 3 (92 - 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 8 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 3 (92 - 8 ((- 4) (- 2) - 5 \cdot - 5) - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $- 2$ .

$5728 - 1 (- 3 (92 - 8 (8 - 5 \cdot - 5) - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 5$ .

$5728 - 1 (- 3 (92 - 8 (8 + 25) - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $8$ and $25$ .

$5728 - 1 (- 3 (92 - 8 \cdot 33 - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 8$ by $33$ .

$5728 - 1 (- 3 (92 - 264 - 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 3 (92 - 264 - 5 ((- 4) (7) + 6 \cdot - 5)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $7$ .

$5728 - 1 (- 3 (92 - 264 - 5 (- 28 + 6 \cdot - 5)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 5$ .

$5728 - 1 (- 3 (92 - 264 - 5 (- 28 - 30)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $30$ from $- 28$ .

$5728 - 1 (- 3 (92 - 264 - 5 \cdot - 58) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 58$ .

$5728 - 1 (- 3 (92 - 264 + 290) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $264$ from $92$ .

$5728 - 1 (- 3 (- 172 + 290) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 172$ and $290$ .

$5728 - 1 (- 3 \cdot 118 - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $118$ .

$5728 - 1 (- 354 - 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 1 (- 354 - 3 (5 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} | - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 - 3 (5 ((- 6) (- 2) - 5 \cdot 7) - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 6$ by $- 2$ .

$5728 - 1 (- 354 - 3 (5 (12 - 5 \cdot 7) - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $7$ .

$5728 - 1 (- 354 - 3 (5 (12 - 35) - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $35$ from $12$ .

$5728 - 1 (- 354 - 3 (5 \cdot - 23 - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $- 23$ .

$5728 - 1 (- 354 - 3 (- 115 - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 - 3 (- 115 - 8 ((2) (- 2) - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 2$ .

$5728 - 1 (- 354 - 3 (- 115 - 8 (- 4 - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $4$ .

$5728 - 1 (- 354 - 3 (- 115 - 8 (- 4 - 20) - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $20$ from $- 4$ .

$5728 - 1 (- 354 - 3 (- 115 - 8 \cdot - 24 - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 8$ by $- 24$ .

$5728 - 1 (- 354 - 3 (- 115 + 192 - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 - 3 (- 115 + 192 - 5 ((2) (7) + 6 \cdot 4)) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $7$ .

$5728 - 1 (- 354 - 3 (- 115 + 192 - 5 (14 + 6 \cdot 4)) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $4$ .

$5728 - 1 (- 354 - 3 (- 115 + 192 - 5 (14 + 24)) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $14$ and $24$ .

$5728 - 1 (- 354 - 3 (- 115 + 192 - 5 \cdot 38) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $38$ .

$5728 - 1 (- 354 - 3 (- 115 + 192 - 190) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 115$ and $192$ .

$5728 - 1 (- 354 - 3 (77 - 190) - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $190$ from $77$ .

$5728 - 1 (- 354 - 3 \cdot - 113 - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 113$ .

$5728 - 1 (- 354 + 339 - 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 1 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 1 (- 354 + 339 - 1 (5 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 + 339 - 1 (5 ((- 4) (- 2) - 5 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $- 2$ .

$5728 - 1 (- 354 + 339 - 1 (5 (8 - 5 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 5$ .

$5728 - 1 (- 354 + 339 - 1 (5 (8 + 25) + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $8$ and $25$ .

$5728 - 1 (- 354 + 339 - 1 (5 \cdot 33 + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $33$ .

$5728 - 1 (- 354 + 339 - 1 (165 + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 + 339 - 1 (165 + 4 ((2) (- 2) - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 2$ .

$5728 - 1 (- 354 + 339 - 1 (165 + 4 (- 4 - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $4$ .

$5728 - 1 (- 354 + 339 - 1 (165 + 4 (- 4 - 20) - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $20$ from $- 4$ .

$5728 - 1 (- 354 + 339 - 1 (165 + 4 \cdot - 24 - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 24$ .

$5728 - 1 (- 354 + 339 - 1 (165 - 96 - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 + 339 - 1 (165 - 96 - 5 ((2) (- 5) + 4 \cdot 4)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 5$ .

$5728 - 1 (- 354 + 339 - 1 (165 - 96 - 5 (- 10 + 4 \cdot 4)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $4$ .

$5728 - 1 (- 354 + 339 - 1 (165 - 96 - 5 (- 10 + 16)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 10$ and $16$ .

$5728 - 1 (- 354 + 339 - 1 (165 - 96 - 5 \cdot 6) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $6$ .

$5728 - 1 (- 354 + 339 - 1 (165 - 96 - 30) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $96$ from $165$ .

$5728 - 1 (- 354 + 339 - 1 (69 - 30) - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $30$ from $69$ .

$5728 - 1 (- 354 + 339 - 1 \cdot 39 - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 1$ by $39$ .

$5728 - 1 (- 354 + 339 - 39 - 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 1 (- 354 + 339 - 39 - 3 (5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} | + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (5 ((- 4) (7) + 6 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $7$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (5 (- 28 + 6 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 5$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (5 (- 28 - 30) + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $30$ from $- 28$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (5 \cdot - 58 + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $- 58$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 4 ((2) (7) + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $7$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 4 (14 + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $4$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 4 (14 + 24) + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $14$ and $24$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 4 \cdot 38 + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $38$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 152 + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 152 + 8 ((2) (- 5) + 4 \cdot 4))) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 5$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 152 + 8 (- 10 + 4 \cdot 4))) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $4$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 152 + 8 (- 10 + 16))) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 10$ and $16$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 152 + 8 \cdot 6)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $8$ by $6$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 290 + 152 + 48)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 290$ and $152$ .

$5728 - 1 (- 354 + 339 - 39 - 3 (- 138 + 48)) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 138$ and $48$ .

$5728 - 1 (- 354 + 339 - 39 - 3 \cdot - 90) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 90$ .

$5728 - 1 (- 354 + 339 - 39 + 270) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 354$ and $339$ .

$5728 - 1 (- 15 - 39 + 270) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $39$ from $- 15$ .

$5728 - 1 (- 54 + 270) + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 54$ and $270$ .

$5728 - 1 \cdot 216 + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 1$ by $216$ .

$5728 - 216 + 7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} | - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $7 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ - 1 & 8 & - 6 & 7 \\ 3 & - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 7 (- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 7 (- 3 (3 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} | - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $3 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (- 3 (3 ((- 6) (- 2) - 5 \cdot 7) - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 6$ by $- 2$ .

$5728 - 216 + 7 (- 3 (3 (12 - 5 \cdot 7) - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $7$ .

$5728 - 216 + 7 (- 3 (3 (12 - 35) - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $35$ from $12$ .

$5728 - 216 + 7 (- 3 (3 \cdot - 23 - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $3$ by $- 23$ .

$5728 - 216 + 7 (- 3 (- 69 - 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 8 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (- 3 (- 69 - 8 ((- 5) (- 2) - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 2$ .

$5728 - 216 + 7 (- 3 (- 69 - 8 (10 - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 3$ .

$5728 - 216 + 7 (- 3 (- 69 - 8 (10 + 15) - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $10$ and $15$ .

$5728 - 216 + 7 (- 3 (- 69 - 8 \cdot 25 - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 8$ by $25$ .

$5728 - 216 + 7 (- 3 (- 69 - 200 - 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (- 3 (- 69 - 200 - 5 ((- 5) (7) + 6 \cdot - 3)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $7$ .

$5728 - 216 + 7 (- 3 (- 69 - 200 - 5 (- 35 + 6 \cdot - 3)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 3$ .

$5728 - 216 + 7 (- 3 (- 69 - 200 - 5 (- 35 - 18)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $18$ from $- 35$ .

$5728 - 216 + 7 (- 3 (- 69 - 200 - 5 \cdot - 53) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 53$ .

$5728 - 216 + 7 (- 3 (- 69 - 200 + 265) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $200$ from $- 69$ .

$5728 - 216 + 7 (- 3 (- 269 + 265) - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 269$ and $265$ .

$5728 - 216 + 7 (- 3 \cdot - 4 - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 4$ .

$5728 - 216 + 7 (12 - 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} | - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 6 | \begin{array}{c} 5 & 2 & 4 \\ 8 & - 6 & 7 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 7 (12 - 6 (5 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} | - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 6 & 7 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 - 6 (5 ((- 6) (- 2) - 5 \cdot 7) - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 6$ by $- 2$ .

$5728 - 216 + 7 (12 - 6 (5 (12 - 5 \cdot 7) - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $7$ .

$5728 - 216 + 7 (12 - 6 (5 (12 - 35) - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $35$ from $12$ .

$5728 - 216 + 7 (12 - 6 (5 \cdot - 23 - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $- 23$ .

$5728 - 216 + 7 (12 - 6 (- 115 - 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 8 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 - 6 (- 115 - 8 ((2) (- 2) - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 2$ .

$5728 - 216 + 7 (12 - 6 (- 115 - 8 (- 4 - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $4$ .

$5728 - 216 + 7 (12 - 6 (- 115 - 8 (- 4 - 20) - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $20$ from $- 4$ .

$5728 - 216 + 7 (12 - 6 (- 115 - 8 \cdot - 24 - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 8$ by $- 24$ .

$5728 - 216 + 7 (12 - 6 (- 115 + 192 - 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 - 6 (- 115 + 192 - 5 ((2) (7) + 6 \cdot 4)) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $7$ .

$5728 - 216 + 7 (12 - 6 (- 115 + 192 - 5 (14 + 6 \cdot 4)) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $4$ .

$5728 - 216 + 7 (12 - 6 (- 115 + 192 - 5 (14 + 24)) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $14$ and $24$ .

$5728 - 216 + 7 (12 - 6 (- 115 + 192 - 5 \cdot 38) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $38$ .

$5728 - 216 + 7 (12 - 6 (- 115 + 192 - 190) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 115$ and $192$ .

$5728 - 216 + 7 (12 - 6 (77 - 190) - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $190$ from $77$ .

$5728 - 216 + 7 (12 - 6 \cdot - 113 - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 6$ by $- 113$ .

$5728 - 216 + 7 (12 + 678 - 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 7 (12 + 678 - 1 (5 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 + 678 - 1 (5 ((- 5) (- 2) - 5 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 2$ .

$5728 - 216 + 7 (12 + 678 - 1 (5 (10 - 5 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 3$ .

$5728 - 216 + 7 (12 + 678 - 1 (5 (10 + 15) - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $10$ and $15$ .

$5728 - 216 + 7 (12 + 678 - 1 (5 \cdot 25 - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $25$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 - 3 ((2) (- 2) - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 2$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 - 3 (- 4 - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $4$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 - 3 (- 4 - 20) - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $20$ from $- 4$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 - 3 \cdot - 24 - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 24$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 + 72 - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 + 72 - 5 ((2) (- 3) + 5 \cdot 4)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 3$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 + 72 - 5 (- 6 + 5 \cdot 4)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $4$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 + 72 - 5 (- 6 + 20)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 6$ and $20$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 + 72 - 5 \cdot 14) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $14$ .

$5728 - 216 + 7 (12 + 678 - 1 (125 + 72 - 70) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $125$ and $72$ .

$5728 - 216 + 7 (12 + 678 - 1 (197 - 70) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $70$ from $197$ .

$5728 - 216 + 7 (12 + 678 - 1 \cdot 127 - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 1$ by $127$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 7 (12 + 678 - 127 - 3 (5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (5 ((- 5) (7) + 6 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $7$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (5 (- 35 + 6 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $- 3$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (5 (- 35 - 18) - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $18$ from $- 35$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (5 \cdot - 53 - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $- 53$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 3 ((2) (7) + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $7$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 3 (14 + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $6$ by $4$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 3 (14 + 24) + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $14$ and $24$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 3 \cdot 38 + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $38$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 114 + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 114 + 8 ((2) (- 3) + 5 \cdot 4))) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 3$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 114 + 8 (- 6 + 5 \cdot 4))) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $4$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 114 + 8 (- 6 + 20))) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 6$ and $20$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 114 + 8 \cdot 14)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $8$ by $14$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 265 - 114 + 112)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $114$ from $- 265$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 (- 379 + 112)) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 379$ and $112$ .

$5728 - 216 + 7 (12 + 678 - 127 - 3 \cdot - 267) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 267$ .

$5728 - 216 + 7 (12 + 678 - 127 + 801) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $12$ and $678$ .

$5728 - 216 + 7 (690 - 127 + 801) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $127$ from $690$ .

$5728 - 216 + 7 (563 + 801) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $563$ and $801$ .

$5728 - 216 + 7 (1364) - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $7$ by $1364$ .

$5728 - 216 + 9548 - 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} | + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 2 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ 3 & - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 - 2 (- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 - 2 (- 3 (3 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $3 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 3 (3 ((- 4) (- 2) - 5 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $- 2$ .

$5728 - 216 + 9548 - 2 (- 3 (3 (8 - 5 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 5$ .

$5728 - 216 + 9548 - 2 (- 3 (3 (8 + 25) + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $8$ and $25$ .

$5728 - 216 + 9548 - 2 (- 3 (3 \cdot 33 + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $3$ by $33$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 4 ((- 5) (- 2) - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 2$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 4 (10 - 5 \cdot - 3) - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 3$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 4 (10 + 15) - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $10$ and $15$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 4 \cdot 25 - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $25$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 100 - 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 100 - 5 ((- 5) (- 5) + 4 \cdot - 3)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 100 - 5 (25 + 4 \cdot - 3)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 3$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 100 - 5 (25 - 12)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $12$ from $25$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 100 - 5 \cdot 13) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $13$ .

$5728 - 216 + 9548 - 2 (- 3 (99 + 100 - 65) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $99$ and $100$ .

$5728 - 216 + 9548 - 2 (- 3 (199 - 65) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $65$ from $199$ .

$5728 - 216 + 9548 - 2 (- 3 \cdot 134 - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $134$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 - 2 (- 402 - 6 (5 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} | + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 4 & - 5 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (5 ((- 4) (- 2) - 5 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $- 2$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (5 (8 - 5 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 5$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (5 (8 + 25) + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $8$ and $25$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (5 \cdot 33 + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $33$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 + 4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $4 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 + 4 ((2) (- 2) - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 2$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 + 4 (- 4 - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $4$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 + 4 (- 4 - 20) - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $20$ from $- 4$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 + 4 \cdot - 24 - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 24$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 - 96 - 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 - 96 - 5 ((2) (- 5) + 4 \cdot 4)) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 5$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 - 96 - 5 (- 10 + 4 \cdot 4)) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $4$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 - 96 - 5 (- 10 + 16)) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 10$ and $16$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 - 96 - 5 \cdot 6) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $6$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (165 - 96 - 30) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $96$ from $165$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 (69 - 30) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $30$ from $69$ .

$5728 - 216 + 9548 - 2 (- 402 - 6 \cdot 39 + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 6$ by $39$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} | - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 5 & 5 & - 2 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (5 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} | - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 5 & - 3 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (5 ((- 5) (- 2) - 5 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 2$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (5 (10 - 5 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $- 3$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (5 (10 + 15) - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $10$ and $15$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (5 \cdot 25 - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $25$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 - 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} | - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 2 & 4 \\ 5 & - 2 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 - 3 ((2) (- 2) - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 2$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 - 3 (- 4 - 5 \cdot 4) - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $4$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 - 3 (- 4 - 20) - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $20$ from $- 4$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 - 3 \cdot - 24 - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 24$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 + 72 - 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 5 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 + 72 - 5 ((2) (- 3) + 5 \cdot 4)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 3$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 + 72 - 5 (- 6 + 5 \cdot 4)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $4$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 + 72 - 5 (- 6 + 20)) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 6$ and $20$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 + 72 - 5 \cdot 14) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 5$ by $14$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (125 + 72 - 70) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $125$ and $72$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (197 - 70) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $70$ from $197$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 3 (127) - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $3$ by $127$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} | - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (5 ((- 5) (- 5) + 4 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (5 (25 + 4 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $- 3$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (5 (25 - 12) - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Subtract $12$ from $25$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (5 \cdot 13 - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $13$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 3 ((2) (- 5) + 4 \cdot 4) - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 5$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 3 (- 10 + 4 \cdot 4) - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $4$ by $4$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 3 (- 10 + 16) - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 10$ and $16$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 3 \cdot 6 - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $6$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 18 - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $- 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 18 - 4 ((2) (- 3) + 5 \cdot 4))) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 3$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 18 - 4 (- 6 + 5 \cdot 4))) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $5$ by $4$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 18 - 4 (- 6 + 20))) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Simplify the expression.

Add $- 6$ and $20$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 18 - 4 \cdot 14)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 4$ by $14$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (65 - 18 - 56)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $18$ from $65$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 (47 - 56)) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $56$ from $47$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 - 3 \cdot - 9) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 3$ by $- 9$ .

$5728 - 216 + 9548 - 2 (- 402 - 234 + 381 + 27) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Subtract $234$ from $- 402$ .

$5728 - 216 + 9548 - 2 (- 636 + 381 + 27) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 636$ and $381$ .

$5728 - 216 + 9548 - 2 (- 255 + 27) + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Add $- 255$ and $27$ .

$5728 - 216 + 9548 - 2 \cdot - 228 + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Multiply $- 2$ by $- 228$ .

$5728 - 216 + 9548 + 456 + 6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$

Find the determinant of $6 | \begin{array}{c} - 3 & 5 & 2 & 4 \\ 6 & 3 & - 5 & - 3 \\ 3 & - 4 & - 4 & - 5 \\ - 1 & 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 + 456 + 6 (- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $- 3 | \begin{array}{c} 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 + 456 + 6 (- 3 (3 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} | + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $3 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (3 ((- 4) (7) + 6 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $7$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (3 (- 28 + 6 \cdot - 5) + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $6$ by $- 5$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (3 (- 28 - 30) + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Subtract $30$ from $- 28$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (3 \cdot - 58 + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $3$ by $- 58$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 + 4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $4 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 + 4 ((- 5) (7) + 6 \cdot - 3) + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $7$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 + 4 (- 35 + 6 \cdot - 3) + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $6$ by $- 3$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 + 4 (- 35 - 18) + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Subtract $18$ from $- 35$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 + 4 \cdot - 53 + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $4$ by $- 53$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 - 212 + 8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $8 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 - 212 + 8 ((- 5) (- 5) + 4 \cdot - 3)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 - 212 + 8 (25 + 4 \cdot - 3)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $4$ by $- 3$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 - 212 + 8 (25 - 12)) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Subtract $12$ from $25$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 - 212 + 8 \cdot 13) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $8$ by $13$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 174 - 212 + 104) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Subtract $212$ from $- 174$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 (- 386 + 104) - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Add $- 386$ and $104$ .

$5728 - 216 + 9548 + 456 + 6 (- 3 \cdot - 282 - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $- 3$ by $- 282$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} | + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $- 6 | \begin{array}{c} 5 & 2 & 4 \\ - 4 & - 4 & - 5 \\ 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} | + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $5 | \begin{array}{c} - 4 & - 5 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (5 ((- 4) (7) + 6 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $7$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (5 (- 28 + 6 \cdot - 5) + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $6$ by $- 5$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (5 (- 28 - 30) + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Subtract $30$ from $- 28$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (5 \cdot - 58 + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $5$ by $- 58$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $4 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 4 ((2) (7) + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $7$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 4 (14 + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $6$ by $4$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 4 (14 + 24) + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Add $14$ and $24$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 4 \cdot 38 + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $4$ by $38$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 152 + 8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $8 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 152 + 8 ((2) (- 5) + 4 \cdot 4)) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 5$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 152 + 8 (- 10 + 4 \cdot 4)) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $4$ by $4$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 152 + 8 (- 10 + 16)) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Add $- 10$ and $16$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 152 + 8 \cdot 6) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $8$ by $6$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 290 + 152 + 48) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Add $- 290$ and $152$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 (- 138 + 48) + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Add $- 138$ and $48$ .

$5728 - 216 + 9548 + 456 + 6 (846 - 6 \cdot - 90 + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $- 6$ by $- 90$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} | + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $3 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ 8 & - 6 & 7 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} | - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $5 | \begin{array}{c} - 5 & - 3 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (5 ((- 5) (7) + 6 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $7$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (5 (- 35 + 6 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $6$ by $- 3$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (5 (- 35 - 18) - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Subtract $18$ from $- 35$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (5 \cdot - 53 - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $5$ by $- 53$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} | + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $- 3 | \begin{array}{c} 2 & 4 \\ - 6 & 7 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 3 ((2) (7) + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $7$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 3 (14 + 6 \cdot 4) + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $6$ by $4$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 3 (14 + 24) + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Add $14$ and $24$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 3 \cdot 38 + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $- 3$ by $38$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 114 + 8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $8 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 114 + 8 ((2) (- 3) + 5 \cdot 4)) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 3$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 114 + 8 (- 6 + 5 \cdot 4)) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $5$ by $4$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 114 + 8 (- 6 + 20)) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Simplify the expression.

Add $- 6$ and $20$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 114 + 8 \cdot 14) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $8$ by $14$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 265 - 114 + 112) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Subtract $114$ from $- 265$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 379 + 112) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Add $- 379$ and $112$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 + 3 (- 267) + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Multiply $3$ by $- 267$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |)$

Find the determinant of $1 | \begin{array}{c} 5 & 2 & 4 \\ 3 & - 5 & - 3 \\ - 4 & - 4 & - 5 \end{array} |$ .

Set up the determinant by breaking it into smaller components.

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} | - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Find the determinant of $5 | \begin{array}{c} - 5 & - 3 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (5 ((- 5) (- 5) + 4 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (5 (25 + 4 \cdot - 3) - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Multiply $4$ by $- 3$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (5 (25 - 12) - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Simplify the expression.

Subtract $12$ from $25$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (5 \cdot 13 - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Multiply $5$ by $13$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} | - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Find the determinant of $- 3 | \begin{array}{c} 2 & 4 \\ - 4 & - 5 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 3 ((2) (- 5) + 4 \cdot 4) - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 5$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 3 (- 10 + 4 \cdot 4) - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Multiply $4$ by $4$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 3 (- 10 + 16) - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Simplify the expression.

Add $- 10$ and $16$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 3 \cdot 6 - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Multiply $- 3$ by $6$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 18 - 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |))$

Find the determinant of $- 4 | \begin{array}{c} 2 & 4 \\ - 5 & - 3 \end{array} |$ .

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 18 - 4 ((2) (- 3) + 5 \cdot 4)))$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 3$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 18 - 4 (- 6 + 5 \cdot 4)))$

Multiply $5$ by $4$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 18 - 4 (- 6 + 20)))$

Simplify the expression.

Add $- 6$ and $20$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 18 - 4 \cdot 14))$

Multiply $- 4$ by $14$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (65 - 18 - 56))$

Subtract $18$ from $65$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 (47 - 56))$

Subtract $56$ from $47$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 + 1 \cdot - 9)$

Multiply $- 9$ by $1$ .

$5728 - 216 + 9548 + 456 + 6 (846 + 540 - 801 - 9)$

Add $846$ and $540$ .

$5728 - 216 + 9548 + 456 + 6 (1386 - 801 - 9)$

Subtract $801$ from $1386$ .

$5728 - 216 + 9548 + 456 + 6 (585 - 9)$

Subtract $9$ from $585$ .

$5728 - 216 + 9548 + 456 + 6 (576)$

Multiply $6$ by $576$ .

$5728 - 216 + 9548 + 456 + 3456$

Subtract $216$ from $5728$ .

$5512 + 9548 + 456 + 3456$

Add $5512$ and $9548$ .

$15060 + 456 + 3456$

Add $15060$ and $456$ .

$15516 + 3456$

Add $15516$ and $3456$ .

$18972$

Find the Determinant [[4,-3,5,2,4],[1,6,3,-5,-3],[7,3,-4,-4,-5],[2,-1,8,-6,7],[6,3,-5,5,-2]]

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