0008.tex

\begin{exercise}{E2}{Reduced row echelon form}{0008}
\begin{exerciseStatement}

\begin{enumerate}[(a)]
\item Show that \[\operatorname{RREF} \left[\begin{array}{ccc}
0 & 5 & 5 \\
-1 & -3 & -4 \\
-1 & 1 & 0 \\
-1 & -8 & -9 \\
-1 & -2 & -3
\end{array}\right] = \left[\begin{array}{ccc}
1 & 0 & 1 \\
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{array}\right] .\]
\item Explain why the matrix \(B= \left[\begin{array}{ccc}
-3 & 15 & 0 \\
0 & 0 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{array}\right] \) is or is not in reduced row echelon form.
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \(\operatorname{RREF} \left[\begin{array}{ccc}
0 & 5 & 5 \\
-1 & -3 & -4 \\
-1 & 1 & 0 \\
-1 & -8 & -9 \\
-1 & -2 & -3
\end{array}\right] = \left[\begin{array}{ccc}
1 & 0 & 1 \\
0 & 1 & 1 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{array}\right] .\)
\item \(B\) is not in reduced row echelon form because the pivots are not all \(1\). 
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}