0007.tex

\begin{exercise}{G1}{Row operations and determinants}{0007}
\begin{exerciseStatement}

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



\begin{enumerate}[(a)]
\item Let \(P\) be the matrix obtained from \(A\) by applying the row operation \( R_4 \to R_4 + 5R_1 \). What is \(\operatorname{det}\ P\)?
\item Let \(B\) be the matrix obtained from \(A\) by applying the row operation \( R_2 \leftrightarrow R_1 \). What is \(\operatorname{det}\ B\)?
\item Let \(M\) be the matrix obtained from \(A\) by applying the row operation \( R_3 \to 3R_3 \). What is \(\operatorname{det}\ M\)?
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \(\operatorname{det}\ P= 6 \)
\item \(\operatorname{det}\ B= -6 \)
\item \(\operatorname{det}\ M= 18 \)
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}