Find the Determinant [[5,1,0],[5,-5,1],[4,-1,0]]

$[\begin{array}{c} 5 & 1 & 0 \\ 5 & - 5 & 1 \\ 4 & - 1 & 0 \end{array}]$

Step 1

Multiply every element in the $3 r d$ column by its cofactor and add.

$0 | \begin{array}{c} 5 & - 5 \\ 4 & - 1 \end{array} | - | \begin{array}{c} 5 & 1 \\ 4 & - 1 \end{array} | + 0 | \begin{array}{c} 5 & 1 \\ 5 & - 5 \end{array} |$

Step 2

Multiply $0$ by $| \begin{array}{c} 5 & - 5 \\ 4 & - 1 \end{array} |$ .

$0 - | \begin{array}{c} 5 & 1 \\ 4 & - 1 \end{array} | + 0 | \begin{array}{c} 5 & 1 \\ 5 & - 5 \end{array} |$

Step 3

Multiply $0$ by $| \begin{array}{c} 5 & 1 \\ 5 & - 5 \end{array} |$ .

$0 - | \begin{array}{c} 5 & 1 \\ 4 & - 1 \end{array} | + 0$

Step 4

Evaluate $| \begin{array}{c} 5 & 1 \\ 4 & - 1 \end{array} |$ .

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

$0 - (5 \cdot - 1 - 4 \cdot 1) + 0$

Simplify the determinant.

Simplify each term.

Multiply $5$ by $- 1$ .

$0 - (- 5 - 4 \cdot 1) + 0$

Multiply $- 4$ by $1$ .

$0 - (- 5 - 4) + 0$

Subtract $4$ from $- 5$ .

$0 - - 9 + 0$

Step 5

Simplify the determinant.

Multiply $- 1$ by $- 9$ .

$0 + 9 + 0$

Add $0$ and $9$ .

$9 + 0$

Add $9$ and $0$ .

$9$

Find the Determinant [[5,1,0],[5,-5,1],[4,-1,0]]

Related Questions

Support LCMGCF.com by disabling your adblocker.