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\begin{document}
\noindent Name: \rule{7cm}{.2pt} \vspace{.3cm} \hfill Date:  \rule{3.5cm}{.2pt}
\vspace{.3cm}

\noindent\hrulefill
\begin{center}
{\bf \Large{MA 162}} \\\vspace{.1cm} Week 6 Recitation Worksheet (Thursday)
\end{center}
\vspace{-.3cm}
\hrulefill

\begin{center}
\fbox{\textbf{You must show all work to receive full credit.}}
\end{center}

\begin{enumerate}[ref=\#\arabic*]
%1
\item Define $A$, $B$ and $C$ as
\begin{equation*}
A = \left[\begin{array}{rr}
a & 5\\
6 & 8\\
2 & -9
\end{array}\right], \quad 
B = \left[\begin{array}{rrr}
1 & -4 & b\\
c & 7 & -3
\end{array}\right], \quad
C = \left[\begin{array}{rrr}
-2 & 0 & 3\\
4 & d & -1
\end{array}\right],
\end{equation*}
where $a,b,c,d$ are real numbers.   Determine the following matrices, if possible.  If a matrix is undefined, explain why the matrix operation cannot be performed.
\begin{parts}
\part $B - C$\vfill\vfill
\part $3A$\vfill\vfill
\part $BC$\vfill\vfill
\part $CA$\vfill\vfill\vfill
\end{parts}


\newpage
%2
\item Solve the following system of equations using the Gauss-Jordan method.
$$\left\{ \begin{array}{rcrcr}
x & - & 3y & = & -25 \\
5x & + & 2y & = & 11
\end{array} \right. $$
\begin{parts}
\part Write down the augmented matrix.\vfill
\part Perform the following row operation to the previous matrix: $R_2 \to R_2 - 5R_1$.\vfill
\part Perform the following row operation to the previous matrix: $R_2 \to \frac{1}{17}R_2$.\vfill
\part Perform the following row operation to the previous matrix: $R_1 \to R_1 + 3R_2$.\vfill
\part What is the solution $(x,y)$ to the system of equations? [Compare this answer with your answer from \#1 on last week's worksheet.]\vfill
\end{parts}


\newpage
%3
\item Solve the following system of equations using the Gauss-Jordan method.
$$\left\{ \begin{array}{rcrcrcr}
x & - & 2y & + & 3z & = & -1 \\
-2x & + & 5y & - & 10z & = & 4 \\
7x & - & 17y & + & 35z & = & -19
\end{array} \right. $$
\end{enumerate}
\end{document}