<exercise>
<statement>
<ol>
<li>Show that <me>\operatorname{RREF}<xsl:value-of select="A"/>=<xsl:value-of select="rref"/>.</me></li>
<li>Explain why the matrix <m>B=<xsl:value-of select="B"/></m> is or is not in reduced row echelon form.</li>
</ol>
</statement>
<answer>
<ol>
<li><m>\operatorname{RREF}<xsl:value-of select="A"/>=<xsl:value-of select="rref"/>.</m></li>
<li>
<m>B</m> is
<xsl:choose>
<xsl:when test="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.
</xsl:when>
<xsl:otherwise>
not in reduced row echelon form because
<xsl:choose>
<xsl:when test="rowop='elementary'">
not every entry above and below each pivot is zero.
</xsl:when>
<xsl:when test="rowop='permutation'">
the pivots are not descending to the right.
</xsl:when>
<xsl:otherwise>
the pivots are not all <m>1</m>.
</xsl:otherwise>
</xsl:choose>
</xsl:otherwise>
</xsl:choose>
</li>
</ol>
</answer>
</exercise>
