0001.tex

\begin{exercise}{A1}{Linear maps}{0001}
\begin{exerciseStatement}

Consider the following maps of polynomials \(S:\mathcal{P}\rightarrow\mathcal{P}\) and \(T:\mathcal{P}\rightarrow\mathcal{P}\) defined by \[
                S(g(x))=
     -3 \, g\left(1\right) + 5 \, g\left(x^{2}\right) 
                \hspace{1em} \text{and} \hspace{1em} T(g(x))=
     -3 \, g\left(x\right)^{3} - 2 \, g'\left(x\right) \] Explain why one these maps is a linear transformation and why the other map is not. 

\end{exerciseStatement}
\begin{exerciseAnswer}

\(S\) is linear and \(T\) is not linear.

\end{exerciseAnswer}
\end{exercise}