0006.tex

\begin{exercise}{E1}{Linear systems, vector equations, and augmented matrices}{0006}
\begin{exerciseStatement}

 Consider the system of equations

\[\begin{matrix}
 x_{1} &  &  &  -  & x_{3} & = & 3 \\
 5 \, x_{1} &  +  & x_{2} &  &  & = & 8 \\
 -x_{1} &  -  & x_{2} &  -  & 3 \, x_{3} & = & 3 \\
 -2 \, x_{1} &  -  & x_{2} &  +  & x_{3} & = & -3 \\
 \end{matrix}\]

\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 \[ \left[\begin{array}{ccc|c}
1 & 0 & -1 & 3 \\
5 & 1 & 0 & 8 \\
-1 & -1 & -3 & 3 \\
-2 & -1 & 1 & -3
\end{array}\right] \]
\item \[ x_{1} \left[\begin{array}{c}
1 \\
5 \\
-1 \\
-2
\end{array}\right] + x_{2} \left[\begin{array}{c}
0 \\
1 \\
-1 \\
-1
\end{array}\right] + x_{3} \left[\begin{array}{c}
-1 \\
0 \\
-3 \\
1
\end{array}\right] = \left[\begin{array}{c}
3 \\
8 \\
3 \\
-3
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}