<exercise checkit-seed="0012" checkit-slug="E2" checkit-title="Reduced row echelon form">
<statement>
<ol>
<li>Show that <me>\operatorname{RREF} \left[\begin{array}{cccc}
0 & 1 & 1 & 5 \\
-1 & -2 & -1 & -5 \\
0 & -2 & -1 & -6 \\
-2 & -2 & -2 & -8
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 0 & -1 \\
0 & 1 & 0 & 1 \\
0 & 0 & 1 & 4 \\
0 & 0 & 0 & 0
\end{array}\right] .</me></li>
<li>Explain why the matrix <m>B= \left[\begin{array}{cccc}
-7 & 0 & 0 & 0 \\
0 & 1 & 0 & 2 \\
0 & 0 & 1 & 1 \\
0 & 0 & 0 & 0
\end{array}\right] </m> is or is not in reduced row echelon form.</li>
</ol>
</statement>
<answer>
<ol>
<li>
<m>\operatorname{RREF} \left[\begin{array}{cccc}
0 & 1 & 1 & 5 \\
-1 & -2 & -1 & -5 \\
0 & -2 & -1 & -6 \\
-2 & -2 & -2 & -8
\end{array}\right] = \left[\begin{array}{cccc}
1 & 0 & 0 & -1 \\
0 & 1 & 0 & 1 \\
0 & 0 & 1 & 4 \\
0 & 0 & 0 & 0
\end{array}\right] .</m>
</li>
<li><m>B</m> is
not in reduced row echelon form because
the pivots are not all <m>1</m>.
</li>
</ol>
</answer>
</exercise>
