Find the Determinant [[2,-4],[7,3]]

$[\begin{array}{c} 2 & - 4 \\ 7 & 3 \end{array}]$

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

$determinant [\begin{array}{c} 2 & - 4 \\ 7 & 3 \end{array}] = | \begin{array}{c} 2 & - 4 \\ 7 & 3 \end{array} |$

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

$(2) (3) - 7 \cdot - 4$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $3$ .

$6 - 7 \cdot - 4$

Multiply $- 7$ by $- 4$ .

$6 + 28$

Add $6$ and $28$ .

$34$