0004.tex

\begin{exercise}{E1}{Linear systems, vector equations, and augmented matrices}{0004}
\begin{exerciseStatement}

 Consider the system of equations

\[\begin{matrix}
 -3 \, x &  -  & y &  +  & 7 \, z & = & 1 \\
 &  & y &  -  & 5 \, z & = & 6 \\
 -x &  &  &  +  & 3 \, z & = & 0 \\
 -2 \, x &  -  & y &  +  & 7 \, z & = & -2 \\
 \end{matrix}\]

\begin{enumerate}[(a)]
\item  Write an augmented matrix corresponding to this system. 
\item  Write a vector equation corresponding to this system. 
\end{enumerate}

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \[ \left[\begin{array}{ccc|c}
-3 & -1 & 7 & 1 \\
0 & 1 & -5 & 6 \\
-1 & 0 & 3 & 0 \\
-2 & -1 & 7 & -2
\end{array}\right] \]
\item \[ x_{1} \left[\begin{array}{c}
-3 \\
0 \\
-1 \\
-2
\end{array}\right] + x_{2} \left[\begin{array}{c}
-1 \\
1 \\
0 \\
-1
\end{array}\right] + x_{3} \left[\begin{array}{c}
7 \\
-5 \\
3 \\
7
\end{array}\right] = \left[\begin{array}{c}
1 \\
6 \\
0 \\
-2
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}