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

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

Step 1

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

$- 4 \cdot 1 - 2 \cdot 5$

Step 2

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $1$ .

$- 4 - 2 \cdot 5$

Multiply $- 2$ by $5$ .

$- 4 - 10$

Subtract $10$ from $- 4$ .

$- 14$