Chapter 12 - Matrices - 12-3 Determinants and Inverses - Practice and Problem-Solving Exercises - Page 788: 12

$-21$

The determinant of a $2\times2$ matrix $A=\begin{bmatrix}a & b\\c&d \end{bmatrix}$ is given by $ad-bc.$ Hence, the determinant of the given matrix, $ \begin{bmatrix} 7&2\\0&-3 \end{bmatrix}$ is \begin{align*} & 7(-3)-0(2) \\&= -21-0 \\&= -21 .\end{align*}