0003.ptx

<exercise checkit-seed="0003" 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(g(x))=
     x^{3} g\left(x\right) + 2 \, g\left(x\right)^{3} 
                \hspace{1em} \text{and} \hspace{1em} T(g(x))=
     -3 \, g\left(x^{3}\right) + 2 \, g'\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 not linear and <m>T</m> is linear.</p>
  </answer>
</exercise>