\begin{exercise}{M4}{Finding a matrix inverse}{0010}
\begin{exerciseStatement}
Show how to find the inverse of the matrix \(A= \left[\begin{array}{cccc}
1 & -1 & 3 & 5 \\
0 & 1 & -5 & -8 \\
0 & 0 & 1 & 2 \\
0 & 1 & -3 & -3
\end{array}\right] \).
\end{exerciseStatement}
\begin{exerciseAnswer}\[A^{-1}= \left[\begin{array}{cccc}
1 & 2 & 4 & -1 \\
0 & 3 & 9 & -2 \\
0 & 2 & 5 & -2 \\
0 & -1 & -2 & 1
\end{array}\right] \]\end{exerciseAnswer}
\end{exercise}