\begin{exercise}{G2}{Determinants}{0001}
\begin{exerciseStatement}
Show how to compute the determinant of the matrix \[A= \left[\begin{array}{cccc}
5 & 0 & 1 & 1 \\
-6 & -5 & -3 & 0 \\
2 & 3 & 6 & -2 \\
-6 & 1 & -1 & 0
\end{array}\right] .\].
\end{exerciseStatement}
\begin{exerciseAnswer}\[\operatorname{det}\ \left[\begin{array}{cccc}
5 & 0 & 1 & 1 \\
-6 & -5 & -3 & 0 \\
2 & 3 & 6 & -2 \\
-6 & 1 & -1 & 0
\end{array}\right] = -156 \]\end{exerciseAnswer}
\end{exercise}