0007.tex

\begin{exercise}{A2}{Standard matrices}{0007}
\begin{exerciseStatement}

\begin{enumerate}[(a)]
\item Find the standard matrix for the linear transformation \(S:\mathbb{R}^ 4  \to \mathbb{R}^ 2 \) given by \[S\left(  \left[\begin{array}{c}
x \\
y \\
z \\
{w}
\end{array}\right]  \right) =  \left[\begin{array}{c}
x - 3 \, y + 5 \, z - 4 \, {w} \\
x - 2 \, y + 4 \, z - 3 \, {w}
\end{array}\right] .\]
\item Let \(T:\mathbb{R}^ 4  \to \mathbb{R}^ 2 \) be the linear transformation given by the standard matrix \[ \left[\begin{array}{cccc}
1 & -2 & -4 & 3 \\
-1 & 3 & 6 & -4
\end{array}\right] .\] Compute \(T\left( \left[\begin{array}{c}
-5 \\
-5 \\
-3 \\
-6
\end{array}\right]  \right)\). 
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \[ \left[\begin{array}{cccc}
1 & -3 & 5 & -4 \\
1 & -2 & 4 & -3
\end{array}\right] \]
\item \[T\left( \left[\begin{array}{c}
-5 \\
-5 \\
-3 \\
-6
\end{array}\right]  \right)= \left[\begin{array}{c}
-1 \\
-4
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}