Find the Determinant [[2,-5],[-1,3]]

$[\begin{array}{c} 2 & - 5 \\ - 1 & 3 \end{array}]$

Step 1

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

$2 \cdot 3 - - - 5$

Step 2

Simplify the determinant.

Simplify each term.

Multiply $2$ by $3$ .

$6 - - - 5$

Multiply $- - - 5$ .

Multiply $- 1$ by $- 5$ .

$6 - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$6 - 5$

Subtract $5$ from $6$ .

$1$