V4.ptx

<exercise>
  <statement>
    <p>Consider the following two sets of Euclidean vectors:
    </p>
    <md>
      <mrow>
          U=<xsl:value-of select="U"/> &amp; &amp;  W=<xsl:value-of select="W"/>
      </mrow>
    </md>
    <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>