\begin{exercise}{M3}{Invertible matrices}{0009}
\begin{exerciseStatement}
Explain why the matrix \(P= \left[\begin{array}{cccc}
-3 & 2 & -6 & 4 \\
-2 & 1 & -3 & 3 \\
5 & 0 & 1 & -8 \\
0 & 3 & -6 & 4
\end{array}\right] \) is or is not invertible.
\end{exerciseStatement}
\begin{exerciseAnswer}
\[\operatorname{RREF} \left[\begin{array}{cccc}
-3 & 2 & -6 & 4 \\
-2 & 1 & -3 & 3 \\
5 & 0 & 1 & -8 \\
0 & 3 & -6 & 4
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \]
\(P\) is invertible.\end{exerciseAnswer}
\end{exercise}
