0000.tex

\begin{exercise}{A2}{Standard matrices}{0000}
\begin{exerciseStatement}

\begin{enumerate}[(a)]
\item Find the standard matrix for the linear transformation \(S:\mathbb{R}^ 2  \to \mathbb{R}^ 4 \) given by \[S\left(  \left[\begin{array}{c}
x \\
y
\end{array}\right]  \right) =  \left[\begin{array}{c}
x - 5 \, y \\
-x + 6 \, y \\
0 \\
x - 2 \, y
\end{array}\right] .\]
\item Let \(T:\mathbb{R}^ 2  \to \mathbb{R}^ 4 \) be the linear transformation given by the standard matrix \[ \left[\begin{array}{cc}
-1 & 0 \\
-1 & -4 \\
2 & 5 \\
-1 & 0
\end{array}\right] .\] Compute \(T\left( \left[\begin{array}{c}
-2 \\
8
\end{array}\right]  \right)\). 
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \[ \left[\begin{array}{cc}
1 & -5 \\
-1 & 6 \\
0 & 0 \\
1 & -2
\end{array}\right] \]
\item \[T\left( \left[\begin{array}{c}
-2 \\
8
\end{array}\right]  \right)= \left[\begin{array}{c}
2 \\
-30 \\
36 \\
2
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}