Find the Determinant [[-1,-3,-2],[4,7,3],[3,9,9]]

$[\begin{array}{c} - 1 & - 3 & - 2 \\ 4 & 7 & 3 \\ 3 & 9 & 9 \end{array}]$

Step 1

Multiply every element in the $1 s t$ row by its cofactor and add.

$- | \begin{array}{c} 7 & 3 \\ 9 & 9 \end{array} | + 3 | \begin{array}{c} 4 & 3 \\ 3 & 9 \end{array} | - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Step 2

Evaluate $| \begin{array}{c} 7 & 3 \\ 9 & 9 \end{array} |$ .

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

$- (7 \cdot 9 - 9 \cdot 3) + 3 | \begin{array}{c} 4 & 3 \\ 3 & 9 \end{array} | - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $7$ by $9$ .

$- (63 - 9 \cdot 3) + 3 | \begin{array}{c} 4 & 3 \\ 3 & 9 \end{array} | - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Multiply $- 9$ by $3$ .

$- (63 - 27) + 3 | \begin{array}{c} 4 & 3 \\ 3 & 9 \end{array} | - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Subtract $27$ from $63$ .

$- 1 \cdot 36 + 3 | \begin{array}{c} 4 & 3 \\ 3 & 9 \end{array} | - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Step 3

Evaluate $| \begin{array}{c} 4 & 3 \\ 3 & 9 \end{array} |$ .

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

$- 1 \cdot 36 + 3 (4 \cdot 9 - 3 \cdot 3) - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $9$ .

$- 1 \cdot 36 + 3 (36 - 3 \cdot 3) - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Multiply $- 3$ by $3$ .

$- 1 \cdot 36 + 3 (36 - 9) - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Subtract $9$ from $36$ .

$- 1 \cdot 36 + 3 \cdot 27 - 2 | \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$

Step 4

Evaluate $| \begin{array}{c} 4 & 7 \\ 3 & 9 \end{array} |$ .

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

$- 1 \cdot 36 + 3 \cdot 27 - 2 (4 \cdot 9 - 3 \cdot 7)$

Simplify the determinant.

Simplify each term.

Multiply $4$ by $9$ .

$- 1 \cdot 36 + 3 \cdot 27 - 2 (36 - 3 \cdot 7)$

Multiply $- 3$ by $7$ .

$- 1 \cdot 36 + 3 \cdot 27 - 2 (36 - 21)$

Subtract $21$ from $36$ .

$- 1 \cdot 36 + 3 \cdot 27 - 2 \cdot 15$

Step 5

Simplify the determinant.

Simplify each term.

Multiply $- 1$ by $36$ .

$- 36 + 3 \cdot 27 - 2 \cdot 15$

Multiply $3$ by $27$ .

$- 36 + 81 - 2 \cdot 15$

Multiply $- 2$ by $15$ .

$- 36 + 81 - 30$

Add $- 36$ and $81$ .

$45 - 30$

Subtract $30$ from $45$ .

$15$

Find the Determinant [[-1,-3,-2],[4,7,3],[3,9,9]]

Related Questions

Support LCMGCF.com by disabling your adblocker.