\begin{exercise}{G2}{Determinants}{0000}
\begin{exerciseStatement}
Show how to compute the determinant of the matrix \[A= \left[\begin{array}{cccc}
-5 & -1 & 5 & 0 \\
-2 & 5 & -3 & 0 \\
-1 & 0 & 3 & 3 \\
-4 & -6 & -6 & -1
\end{array}\right] .\].
\end{exerciseStatement}
\begin{exerciseAnswer}\[\operatorname{det}\ \left[\begin{array}{cccc}
-5 & -1 & 5 & 0 \\
-2 & 5 & -3 & 0 \\
-1 & 0 & 3 & 3 \\
-4 & -6 & -6 & -1
\end{array}\right] = -1141 \]\end{exerciseAnswer}
\end{exercise}