Chapter 3 - Section 3.5 - Determinants and Cramer’s Rule - Exercise Set - Page 240: 32

$-20$

Formula to determine the determinant, $D$ of a $3 \times 3$ matrix is: $D=\begin{vmatrix}a&b&c\\d&e&f\\g&h&i\end{vmatrix}=a \begin{vmatrix}e&f\\h&i\end{vmatrix}-b \begin{vmatrix}d&f\\g&i\end{vmatrix}+c \begin{vmatrix}d&e\\g&h\end{vmatrix}$ Thus, as per question, we have $D=\begin{vmatrix}1&2&3\\2&2&-3\\3&2&1\end{vmatrix}=8-22-6=-20$