0011.tex

\begin{exercise}{M2}{Row operations as matrix multiplication}{0011}
\begin{exerciseStatement}

Let \(A\) be a \(4 \times 4\) matrix.



\begin{enumerate}[(a)]
\item Give a \(4 \times 4\) matrix \(B\) that may be used to perform the row operation \( R_4 \to R_4 + 3R_2 \).
\item Give a \(4 \times 4\) matrix \(Q\) that may be used to perform the row operation \( R_2 \leftrightarrow R_1 \).
\item Use matrix multiplication to describe the matrix obtained by applying \( R_2 \leftrightarrow R_1 \) and then \( R_4 \to R_4 + 3R_2 \) to \(A\) (note the order). 
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \(B= \left[\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 3 & 0 & 1
\end{array}\right] \)
\item \(Q= \left[\begin{array}{cccc}
0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \)
\item \(BQA\)
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}