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\begin{center}
{\Large TEST 3

Math 1090 - 2}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
Use the back of the pages if necessary.
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\item  Find the inverse of the matrix below
\[
A=\left[ \begin{array}{rrr}
-1 & 2 & 1 \\
-5 & 8 & 2 \\
7 & -11 & -3  
\end{array} \right]
\]

\item  Are the two matrices below inverses?
\[
\left[ \begin{array}{rrr}
2 & -1 & -2 \\
3 & -1 & 1 \\
1 & 1 & -1
\end{array} \right]
\hspace{.5in}
\left[ \begin{array}{rrr}
0 &  1/4 & 1/4 \\
-1/3 & 0 & 2/3 \\
-1/3 & 1/4 & -1/12 
\end{array} \right]
\]

\item  Solve the system of equations \underline{using} inverse matrices.

\[
\begin{array}{ccccccc}
2x & - & y & - & 2z & = & 7 \\
3x & - & y & + & z & = & 5 \\
x & + & y & - & z & = & -2 \\
\end{array}
\]

\item  You are working at Gray Whale and sell a bunch of cd's.
You sell some cd's at \$8 each and some at \$9 each.
You end up selling 87 cd's and getting \$732.
How many cd's do you sell at \$8 and how many at \$9?
(You will \underline{not} get credit without setting up the equations.)

\item  For a certain product the revenue function is $R(x)=40x$
and the cost function is $C(x)=20x+1600$.
When is the revenue greater then the profit?

\item  Graph the solution to the inequalities and find all the corners 
of the shaded region.
\begin{eqnarray*}
y - 2x & \leq & 0 \\
2y - x & \leq & 4 \\
 y & \geq & 2 \\
 y & \leq & 6
\end{eqnarray*}

\item Find the maximum and minimum of the function $A=3x-2y$ 
when $x$ and $y$ are in the shaded region of the previous problem.




\end{enumerate}


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