\begin{exercise}{M3}{Invertible matrices}{0008}
\begin{exerciseStatement}
Explain why the matrix \(Q= \left[\begin{array}{cccc}
1 & 1 & -1 & 3 \\
1 & 0 & 1 & 2 \\
-2 & 1 & -4 & -8 \\
0 & -1 & 2 & 2
\end{array}\right] \) is or is not invertible.
\end{exerciseStatement}
\begin{exerciseAnswer}
\[\operatorname{RREF} \left[\begin{array}{cccc}
1 & 1 & -1 & 3 \\
1 & 0 & 1 & 2 \\
-2 & 1 & -4 & -8 \\
0 & -1 & 2 & 2
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 1 & 0 \\
0 & 1 & -2 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0
\end{array}\right] \]
\(Q\) is not invertible.\end{exerciseAnswer}
\end{exercise}
