0002.tex

\begin{exercise}{E1}{Linear systems, vector equations, and augmented matrices}{0002}
\begin{exerciseStatement}

 Consider the augmented matrix 

\[ \left[\begin{array}{ccc|c}
4 & 1 & 7 & 6 \\
-5 & -4 & -6 & -2 \\
-1 & 1 & -3 & -4 \\
-3 & 0 & -6 & -6
\end{array}\right] \]

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

    \end{exerciseStatement}
\begin{exerciseAnswer}

\begin{enumerate}[(a)]
\item \[\begin{matrix}
 4 \, x_{1} &  +  & x_{2} &  +  & 7 \, x_{3} & = & 6 \\
 -5 \, x_{1} &  -  & 4 \, x_{2} &  -  & 6 \, x_{3} & = & -2 \\
 -x_{1} &  +  & x_{2} &  -  & 3 \, x_{3} & = & -4 \\
 -3 \, x_{1} &  &  &  -  & 6 \, x_{3} & = & -6 \\
 \end{matrix}\]
\item \[ x_{1} \left[\begin{array}{c}
4 \\
-5 \\
-1 \\
-3
\end{array}\right] + x_{2} \left[\begin{array}{c}
1 \\
-4 \\
1 \\
0
\end{array}\right] + x_{3} \left[\begin{array}{c}
7 \\
-6 \\
-3 \\
-6
\end{array}\right] = \left[\begin{array}{c}
6 \\
-2 \\
-4 \\
-6
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}