Find the Determinant [[-3,4],[-1,2]]

$[\begin{array}{c} - 3 & 4 \\ - 1 & 2 \end{array}]$

Step 1

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

$determinant [\begin{array}{c} - 3 & 4 \\ - 1 & 2 \end{array}] = | \begin{array}{c} - 3 & 4 \\ - 1 & 2 \end{array} |$

Step 2

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

$(- 3) (2) + 1 \cdot 4$

Step 3

Simplify the determinant.

Simplify each term.

Multiply $- 3$ by $2$ .

$- 6 + 1 \cdot 4$

Multiply $4$ by $1$ .

$- 6 + 4$

Add $- 6$ and $4$ .

$- 2$