0009.tex

\begin{exercise}{E1}{Linear systems, vector equations, and augmented matrices}{0009}
\begin{exerciseStatement}

 Consider the system of equations

\[\begin{matrix}
 x_{1} &  &  &  +  & 3 \, x_{3} & = & -4 \\
 &  & x_{2} &  +  & 3 \, x_{3} & = & -5 \\
 x_{1} &  &  &  +  & 4 \, x_{3} & = & -6 \\
 3 \, x_{1} &  -  & 2 \, x_{2} &  +  & 6 \, x_{3} & = & -8 \\
 \end{matrix}\]

\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 \[ \left[\begin{array}{ccc|c}
1 & 0 & 3 & -4 \\
0 & 1 & 3 & -5 \\
1 & 0 & 4 & -6 \\
3 & -2 & 6 & -8
\end{array}\right] \]
\item \[ x_{1} \left[\begin{array}{c}
1 \\
0 \\
1 \\
3
\end{array}\right] + x_{2} \left[\begin{array}{c}
0 \\
1 \\
0 \\
-2
\end{array}\right] + x_{3} \left[\begin{array}{c}
3 \\
3 \\
4 \\
6
\end{array}\right] = \left[\begin{array}{c}
-4 \\
-5 \\
-6 \\
-8
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}