Find the Determinant [[-5,-4],[2,-10]]

$[\begin{array}{c} - 5 & - 4 \\ 2 & - 10 \end{array}]$

Step 1

These are both valid notations for the determinant of a matrix.

$determinant [\begin{array}{c} - 5 & - 4 \\ 2 & - 10 \end{array}] = | \begin{array}{c} - 5 & - 4 \\ 2 & - 10 \end{array} |$

Step 2

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

$(- 5) (- 10) - 2 \cdot - 4$

Step 3

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 10$ .

$50 - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$50 + 8$

Add $50$ and $8$ .

$58$