<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
<statement>
<ol>
<li>Show that <me>\operatorname{RREF}{{A}}={{rref}}.</me></li>
<li>Explain why the matrix <m>B={{B}}</m> is or is not in reduced row echelon form.</li>
</ol>
</statement>
<answer>
<ol>
<li><me>\operatorname{RREF}{{A}}={{rref}}.</me></li>
<li>
<m>B</m> is
{{#Brref}}
in reduced row echelon form because each pivot is a <m>1</m>, the pivots are descending to the right,
there are zeroes above and below each pivot, and all rows of zeroes are at the bottom.
{{/Brref}}
{{^Brref}}
not in reduced row echelon form because
{{#rowop}}
{{#elementary}}
not every entry above and below each pivot is zero.
{{/elementary}}
{{#permutation}}
the pivots are not descending to the right.
{{/permutation}}
{{#diagonal}}
the pivots are not all <m>1</m>.
{{/diagonal}}
{{/rowop}}
{{/Brref}}
</li>
</ol>
</answer>
</exercise>
