Find the Determinant [[3,-7],[5,2]]

$[\begin{array}{c} 3 & - 7 \\ 5 & 2 \end{array}]$

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

$determinant [\begin{array}{c} 3 & - 7 \\ 5 & 2 \end{array}] = | \begin{array}{c} 3 & - 7 \\ 5 & 2 \end{array} |$

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

$(3) (2) - 5 \cdot - 7$

Simplify the determinant.

Simplify each term.

Multiply $3$ by $2$ .

$6 - 5 \cdot - 7$

Multiply $- 5$ by $- 7$ .

$6 + 35$

Add $6$ and $35$ .

$41$