<exercise>
<statement>
<p>Consider the statement
<claim>
The vector <m><xsl:value-of select="combovector"/></m>
<xsl:choose>
<xsl:when test="statement">is</xsl:when>
<xsl:otherwise>is not</xsl:otherwise>
</xsl:choose>
a linear combination of the vectors <m><xsl:value-of select="veclist"/></m>.
</claim>
</p>
<ol>
<li> Write an equivalent statement using a vector equation.</li>
<li> Explain why your statement is true or false.</li>
</ol>
</statement>
<answer>
<me>\operatorname{RREF} <xsl:value-of select="matrix"/>=<xsl:value-of select="rref"/></me>
<ol>
<li> The statement
<claim>
The vector <m><xsl:value-of select="combovector"/></m>
<xsl:choose>
<xsl:when test="statement">is</xsl:when>
<xsl:otherwise>is not</xsl:otherwise>
</xsl:choose>
a linear combination of the vectors <m><xsl:value-of select="veclist"/></m>.
</claim>
is equivalent to the statement
<claim>
The vector equation <m><xsl:value-of select="veceq"/></m>
<xsl:choose>
<xsl:when test="statement">has a solution.</xsl:when>
<xsl:otherwise>has no solutions.</xsl:otherwise>
</xsl:choose>
</claim>
</li>
<li>
<p> <m><xsl:value-of select="combovector"/></m>
<xsl:choose>
<xsl:when test="lc"> is </xsl:when>
<xsl:otherwise> is not </xsl:otherwise>
</xsl:choose>
a linear combination of the vectors <m><xsl:value-of select="veclist"/></m>.
</p>
</li>
</ol>
</answer>
</exercise>
