0010.tex

\begin{exercise}{E1}{Linear systems, vector equations, and augmented matrices}{0010}
\begin{exerciseStatement}

Consider the vector equation.

\[ x_{1} \left[\begin{array}{c}
1 \\
0 \\
1 \\
0
\end{array}\right] + x_{2} \left[\begin{array}{c}
6 \\
1 \\
-1 \\
2
\end{array}\right] + x_{3} \left[\begin{array}{c}
5 \\
2 \\
-4 \\
2
\end{array}\right] = \left[\begin{array}{c}
-7 \\
-1 \\
0 \\
-2
\end{array}\right] \]

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

    \end{exerciseStatement}
\begin{exerciseAnswer}

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

    \end{exerciseAnswer}
\end{exercise}