\begin{exercise}{M3}{Invertible matrices}{0010}
\begin{exerciseStatement}
Explain why the matrix \(Q= \left[\begin{array}{cccc}
-3 & -3 & 1 & 1 \\
4 & 5 & -2 & -2 \\
-4 & -4 & 1 & 3 \\
-3 & -3 & 0 & 7
\end{array}\right] \) is or is not invertible.
\end{exerciseStatement}
\begin{exerciseAnswer}
\[\operatorname{RREF} \left[\begin{array}{cccc}
-3 & -3 & 1 & 1 \\
4 & 5 & -2 & -2 \\
-4 & -4 & 1 & 3 \\
-3 & -3 & 0 & 7
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \]
\(Q\) is invertible.\end{exerciseAnswer}
\end{exercise}
