<exercise>
<statement>
<p>Consider the following two sets of Euclidean vectors:
</p>
<me>
U=<xsl:value-of select="U"/> \hspace{2em} W=<xsl:value-of select="W"/>
</me>
<p> Explain why one of these sets is a subspace of <m>\mathbb{R}^<xsl:value-of select="dim"/></m> and one is not.
</p>
</statement>
<answer>
<xsl:choose>
<xsl:when test="subspace='U'">
<p><m>U</m> is a subspace of <m>\mathbb{R}^<xsl:value-of select="dim"/></m> and <m>W</m> is not.</p>
</xsl:when>
<xsl:otherwise>
<p><m>W</m> is a subspace of <m>\mathbb{R}^<xsl:value-of select="dim"/></m> and <m>U</m> is not.</p>
</xsl:otherwise>
</xsl:choose>
</answer>
</exercise>
