Answer
24
Work Step by Step
(a) $|A|=\begin{vmatrix}
2 & 3 & -5\\
-4 & 0 & 2\\
6 & -3 & 3
\end{vmatrix}=2.0.3+(-4)(-3)(-5)+6.3.2-(-5).0.6=24$
b) Using elementary row operations:
$|A|=\begin{vmatrix}
2 & 3 & -5\\
-4 & 0 & 2\\
6 & -3 & 3
\end{vmatrix} \approx \begin{vmatrix}
2 & 3 & -5\\
0 & 6 & -8\\
0 & -12 & 18
\end{vmatrix} \approx \begin{vmatrix}
2 & 3 & -5\\
0 & 6 & -8\\
0 & 0 & 2
\end{vmatrix}=24$
c) Using the Cofactor Expansion Theorem
$|A|=A_{13}C_{13}+A_{23}C_{23}=-3.(-24)+3.(-16)=24$
