0004.tex

\begin{exercise}{G1}{Row operations and determinants}{0004}
\begin{exerciseStatement}

Let \(A\) be a \(4 \times 4\) matrix with determinant \( 6 \).



\begin{enumerate}[(a)]
\item Let \(N\) be the matrix obtained from \(A\) by applying the row operation \( R_3 \to -3R_3 \). What is \(\operatorname{det}\ N\)?
\item Let \(Q\) be the matrix obtained from \(A\) by applying the row operation \( R_1 \leftrightarrow R_2 \). What is \(\operatorname{det}\ Q\)?
\item Let \(C\) be the matrix obtained from \(A\) by applying the row operation \( R_1 \to R_1 + 5R_2 \). What is \(\operatorname{det}\ C\)?
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \(\operatorname{det}\ N= -18 \)
\item \(\operatorname{det}\ Q= -6 \)
\item \(\operatorname{det}\ C= 6 \)
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}