Find the Determinant [[-4,1,2],[-1,0,-2],[5,0,1]]

$[\begin{array}{c} - 4 & 1 & 2 \\ - 1 & 0 & - 2 \\ 5 & 0 & 1 \end{array}]$

Step 1

Multiply every element in the $2 n d$ column by its cofactor and add.

$- | \begin{array}{c} - 1 & - 2 \\ 5 & 1 \end{array} | + 0 | \begin{array}{c} - 4 & 2 \\ 5 & 1 \end{array} | + 0 | \begin{array}{c} - 4 & 2 \\ - 1 & - 2 \end{array} |$

Step 2

Multiply $0$ by $| \begin{array}{c} - 4 & 2 \\ 5 & 1 \end{array} |$ .

$- | \begin{array}{c} - 1 & - 2 \\ 5 & 1 \end{array} | + 0 + 0 | \begin{array}{c} - 4 & 2 \\ - 1 & - 2 \end{array} |$

Step 3

Multiply $0$ by $| \begin{array}{c} - 4 & 2 \\ - 1 & - 2 \end{array} |$ .

$- | \begin{array}{c} - 1 & - 2 \\ 5 & 1 \end{array} | + 0 + 0$

Step 4

Evaluate $| \begin{array}{c} - 1 & - 2 \\ 5 & 1 \end{array} |$ .

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

$- (- 1 \cdot 1 - 5 \cdot - 2) + 0 + 0$

Simplify the determinant.

Simplify each term.

Multiply $- 1$ by $1$ .

$- (- 1 - 5 \cdot - 2) + 0 + 0$

Multiply $- 5$ by $- 2$ .

$- (- 1 + 10) + 0 + 0$

Add $- 1$ and $10$ .

$- 1 \cdot 9 + 0 + 0$

Step 5

Simplify the determinant.

Multiply $- 1$ by $9$ .

$- 9 + 0 + 0$

Add $- 9$ and $0$ .

$- 9 + 0$

Add $- 9$ and $0$ .

$- 9$

Find the Determinant [[-4,1,2],[-1,0,-2],[5,0,1]]

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