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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 8 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 \label{B_inv} Use the Gauss-Jordan method to determine the inverse of the matrix
$$A = \left[\begin{array}{rrr}1 & 2 & 3\\0 & 4 & 0\\-5 & -6 & -7\end{array}\right].$$


\newpage
%2
\item Use $A^{-1}$ from \ref{B_inv} to solve the following system of equations.
$$\left\{ \begin{array}{rcrcrcr}
x & + & 2y & + & 3z & = & 8\\
& & 4y &  &  & = & -16\\
-5x & - & 6y & - & 7z & = & 32
\end{array} \right. $$\vspace{1cm}\vfill\vfill


%3
\item An economy has three industries: farming (F), building (B) and clothing (C).  The amount consumed by each sector is given by the following table.
\begin{center}
  \begin{tabular}{ | c | c | c | c |}
    \hline
     & F produces & B produces & C produces \\ \hline
    F consumes & .3 & .2 & .3 \\ \hline
    B consumes & .4 & .4 & .2 \\ \hline
    C consumes & .3 & .4 & .5 \\ \hline
  \end{tabular}
\end{center}
\begin{parts}
\part Write down the internal consumption matrix $A$.\vfill
\part Write down the associated augmented matrix that will be used to solve the closed model.\vfill
\newpage
\part Use the Gauss-Jordan method on the augmented matrix from part (b) to determine how much the farmers and builders produce for every \$17 worth of clothing that is produced.
\end{parts}
\end{enumerate}
\end{document}