0007.tex

\begin{exercise}{E1}{Linear systems, vector equations, and augmented matrices}{0007}
\begin{exerciseStatement}

 Consider the augmented matrix 

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

\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 \[\begin{matrix}
 4 \, x &  +  & 2 \, y &  &  & = & -6 \\
 x &  +  & 2 \, y &  -  & 5 \, z & = & 0 \\
 5 \, x &  +  & 4 \, y &  -  & 6 \, z & = & -6 \\
 -3 \, x &  -  & y &  -  & 2 \, z & = & 5 \\
 \end{matrix}\]
\item \[ x_{1} \left[\begin{array}{c}
4 \\
1 \\
5 \\
-3
\end{array}\right] + x_{2} \left[\begin{array}{c}
2 \\
2 \\
4 \\
-1
\end{array}\right] + x_{3} \left[\begin{array}{c}
0 \\
-5 \\
-6 \\
-2
\end{array}\right] = \left[\begin{array}{c}
-6 \\
0 \\
-6 \\
5
\end{array}\right] \]
\end{enumerate}

    \end{exerciseAnswer}
\end{exercise}