\begin{exercise}{M3}{Invertible matrices}{0007}
\begin{exerciseStatement}
Explain why the matrix \(C= \left[\begin{array}{cccc}
1 & 2 & 1 & -3 \\
-4 & -7 & -3 & 7 \\
-2 & -4 & -1 & 2 \\
-1 & -1 & 1 & -5
\end{array}\right] \) is or is not invertible.
\end{exerciseStatement}
\begin{exerciseAnswer}
\[\operatorname{RREF} \left[\begin{array}{cccc}
1 & 2 & 1 & -3 \\
-4 & -7 & -3 & 7 \\
-2 & -4 & -1 & 2 \\
-1 & -1 & 1 & -5
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \]
\(C\) is invertible.\end{exerciseAnswer}
\end{exercise}
