A1.ptx

<exercise>
  <statement>
    <p>Consider the following maps of polynomials <m>S:\mathcal{P}\rightarrow\mathcal{P}</m> and <m>T:\mathcal{P}\rightarrow\mathcal{P}</m> defined by
    <xsl:choose>
        <xsl:when test="swapped">
            <md>
                <mrow>S(<xsl:value-of select="f_letter"/>(x))=<xsl:value-of select="nonlinear_trans"/> &amp; &amp; \text{and} &amp; &amp; T(<xsl:value-of select="f_letter"/>(x))=<xsl:value-of select="linear_trans"/>.</mrow> 
            </md>
        </xsl:when>
        <xsl:otherwise>
            <md>
                <mrow>S(<xsl:value-of select="f_letter"/>(x))=<xsl:value-of select="linear_trans"/> &amp; &amp; \text{and} &amp;&amp; T(<xsl:value-of select="f_letter"/>(x))=<xsl:value-of select="nonlinear_trans"/>.</mrow> 
            </md>
        </xsl:otherwise>
    </xsl:choose>
    Explain why one these maps is a linear transformation and why the other map is not.
    </p>
  </statement>
  <answer>
    <xsl:choose>
        <xsl:when test="swapped">
            <p><m>S</m> is not linear and <m>T</m> is linear.</p>
        </xsl:when>
        <xsl:otherwise>
            <p><m>S</m> is linear and <m>T</m> is not linear.</p>
        </xsl:otherwise>
    </xsl:choose>
  </answer>
</exercise>