A4.ptx

<exercise>
  <statement>
      Let <m>T:\mathbb{R}^<xsl:value-of select="columns"/> \to \mathbb{R}^<xsl:value-of select="rows"/></m> be the linear transformation given by the standard matrix
      <m><xsl:value-of select="matrix"/>.</m>
      <ol>
            <li>Explain why <m>T</m> is or is not injective.</li>
            <li>Explain why <m>T</m> is or is not surjective.</li>
      </ol>
  </statement>
  <answer>
      <p><me>\operatorname{RREF}<xsl:value-of select="matrix"/>=<xsl:value-of select="rref"/></me></p>
      <ol>
          <li>
              <xsl:choose>
                  <xsl:when test="injective"> <m>T</m> is injective.</xsl:when>
                  <xsl:otherwise> <m>T</m> is not injective</xsl:otherwise>
              </xsl:choose>
          </li>
          <li>
              <xsl:choose>
                  <xsl:when test="surjective"> <m>T</m> is surjective.</xsl:when>
                  <xsl:otherwise> <m>T</m> is not surjective</xsl:otherwise>
              </xsl:choose>
          </li>
      </ol>
  </answer>
</exercise>