\begin{exercise}{G2}{Determinants}{0006}
\begin{exerciseStatement}
Show how to compute the determinant of the matrix \[A= \left[\begin{array}{cccc}
3 & 0 & 4 & -1 \\
-2 & -1 & 0 & 0 \\
-3 & -5 & 2 & 6 \\
6 & 2 & 1 & 3
\end{array}\right] .\].
\end{exerciseStatement}
\begin{exerciseAnswer}\[\operatorname{det}\ \left[\begin{array}{cccc}
3 & 0 & 4 & -1 \\
-2 & -1 & 0 & 0 \\
-3 & -5 & 2 & 6 \\
6 & 2 & 1 & 3
\end{array}\right] = 39 \]\end{exerciseAnswer}
\end{exercise}