0001.tex

\begin{exercise}{G1}{Row operations and determinants}{0001}
\begin{exerciseStatement}

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



\begin{enumerate}[(a)]
\item Let \(N\) be the matrix obtained from \(A\) by applying the row operation \( R_4 \to -5R_4 \). What is \(\operatorname{det}\ N\)?
\item Let \(P\) be the matrix obtained from \(A\) by applying the row operation \( R_3 \to R_3 + -3R_2 \). What is \(\operatorname{det}\ P\)?
\item Let \(C\) be the matrix obtained from \(A\) by applying the row operation \( R_4 \leftrightarrow R_3 \). What is \(\operatorname{det}\ C\)?
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \(\operatorname{det}\ N= 20 \)
\item \(\operatorname{det}\ P= -4 \)
\item \(\operatorname{det}\ C= 4 \)
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}