Find the Determinant [[4,-2],[5,3]]

$[\begin{array}{c} 4 & - 2 \\ 5 & 3 \end{array}]$

Step 1

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

$4 \cdot 3 - 5 \cdot - 2$

Step 2

Simplify the determinant.

Simplify each term.

Multiply $4$ by $3$ .

$12 - 5 \cdot - 2$

Multiply $- 5$ by $- 2$ .

$12 + 10$

Add $12$ and $10$ .

$22$