Find the Determinant [[12,-4,0],[-8,8,0],[4,32,4]]

$[\begin{array}{c} 12 & - 4 & 0 \\ - 8 & 8 & 0 \\ 4 & 32 & 4 \end{array}]$

Step 1

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

$0 | \begin{array}{c} - 8 & 8 \\ 4 & 32 \end{array} | + 0 | \begin{array}{c} 12 & - 4 \\ 4 & 32 \end{array} | + 4 | \begin{array}{c} 12 & - 4 \\ - 8 & 8 \end{array} |$

Step 2

Multiply $0$ by $| \begin{array}{c} - 8 & 8 \\ 4 & 32 \end{array} |$ .

$0 + 0 | \begin{array}{c} 12 & - 4 \\ 4 & 32 \end{array} | + 4 | \begin{array}{c} 12 & - 4 \\ - 8 & 8 \end{array} |$

Step 3

Multiply $0$ by $| \begin{array}{c} 12 & - 4 \\ 4 & 32 \end{array} |$ .

$0 + 0 + 4 | \begin{array}{c} 12 & - 4 \\ - 8 & 8 \end{array} |$

Step 4

Evaluate $| \begin{array}{c} 12 & - 4 \\ - 8 & 8 \end{array} |$ .

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

$0 + 0 + 4 (12 \cdot 8 - (- 8 \cdot - 4))$

Simplify the determinant.

Simplify each term.

Multiply $12$ by $8$ .

$0 + 0 + 4 (96 - (- 8 \cdot - 4))$

Multiply $- (- 8 \cdot - 4)$ .

Multiply $- 8$ by $- 4$ .

$0 + 0 + 4 (96 - 1 \cdot 32)$

Multiply $- 1$ by $32$ .

$0 + 0 + 4 (96 - 32)$

Subtract $32$ from $96$ .

$0 + 0 + 4 \cdot 64$

Step 5

Simplify the determinant.

Multiply $4$ by $64$ .

$0 + 0 + 256$

Add $0$ and $0$ .

$0 + 256$

Add $0$ and $256$ .

$256$

Find the Determinant [[12,-4,0],[-8,8,0],[4,32,4]]

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