0000.tex

\begin{exercise}{G1}{Row operations and determinants}{0000}
\begin{exerciseStatement}

Let \(A\) be a \(4 \times 4\) matrix with determinant \( -2 \).



\begin{enumerate}[(a)]
\item Let \(M\) be the matrix obtained from \(A\) by applying the row operation \( R_1 \to -4R_1 \). What is \(\operatorname{det}\ M\)?
\item Let \(N\) be the matrix obtained from \(A\) by applying the row operation \( R_1 \to R_1 + -3R_2 \). What is \(\operatorname{det}\ N\)?
\item Let \(P\) be the matrix obtained from \(A\) by applying the row operation \( R_1 \leftrightarrow R_4 \). What is \(\operatorname{det}\ P\)?
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \(\operatorname{det}\ M= 8 \)
\item \(\operatorname{det}\ N= -2 \)
\item \(\operatorname{det}\ P= 2 \)
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}