Find the Determinant [[12,-7],[-4,3]]

$[\begin{array}{c} 12 & - 7 \\ - 4 & 3 \end{array}]$

Step 1

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

$12 \cdot 3 - (- 4 \cdot - 7)$

Step 2

Simplify the determinant.

Simplify each term.

Multiply $12$ by $3$ .

$36 - (- 4 \cdot - 7)$

Multiply $- (- 4 \cdot - 7)$ .

Multiply $- 4$ by $- 7$ .

$36 - 1 \cdot 28$

Multiply $- 1$ by $28$ .

$36 - 28$

Subtract $28$ from $36$ .

$8$