A1-9.ptx

<exercise checkit-seed="0009" checkit-slug="A1" checkit-title="Linear maps">
  <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
        <me>
            S(h(x))=
                    5 \, x^{2} h\left(x\right) - h'\left(x\right)
                \hspace{1em} \text{and} \hspace{1em}
            T(h(x))=
                    -2 \, h\left(x\right)^{3} - 4 \, h\left(2\right)
        </me>
        Explain why one these maps is a linear transformation and why the other map is not.
    </p>
  </statement>
  <answer>
            <p><m>S</m> is linear and <m>T</m> is not linear.</p>
  </answer>
</exercise>