0003.tex

\begin{exercise}{M3}{Invertible matrices}{0003}
\begin{exerciseStatement}

Explain why the matrix \(P= \left[\begin{array}{cccc}
1 & 4 & -6 & -4 \\
0 & 1 & -1 & -2 \\
0 & 2 & -1 & -6 \\
0 & 4 & -7 & -1
\end{array}\right] \) is or is not invertible.

\end{exerciseStatement}
\begin{exerciseAnswer}

\[\operatorname{RREF} \left[\begin{array}{cccc}
1 & 4 & -6 & -4 \\
0 & 1 & -1 & -2 \\
0 & 2 & -1 & -6 \\
0 & 4 & -7 & -1
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \]

\(P\) is invertible.\end{exerciseAnswer}
\end{exercise}