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\begin{center}
{\Large TEST 2

Math 1090 - 2}
\end{center}
\vspace{.1in}
You have 1 hour 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.
You will be graded on clarity of answers.
{\bf A correct answer with incorrect or no work is worth no points.}

\vspace{.1in}

Name \rule{5in}{.2pt}

\vspace{.2in}

\begin{enumerate}

\item  SET THIS UP, BUT DO NOT SOLVE IT. 
Make sure you tell me what every variable you use stands for.

An airline company has three type of planes that carry three type of cargo. 
The payload of each plane is:
\[
\begin{array}{c|ccc}
\mbox{type of cargo} & \mbox{Passenger plane} & \mbox{Transport plane} & \mbox{Jumbo Plane} \\
\hline 
\mbox{Mail} & 110 & 90 & 120 \\
\mbox{Passengers} & 140 & 25 & 375 \\
\mbox{Air Freight} & 50 & 60 & 30 
\end{array}
\]
Suppose that the company needs to move exactly 1200 units of mail, 
2910 passengers, and 760 units of air freight.  
How may aircraft of each type is needed?


\item  Find, if possible.  If not possible state why not.
\[
A=\left[ \begin{array}{rrr}
3 & 0 & 1 \\
-2 & 1 & 0
\end{array} \right]\hspace{.5in}
B= \left[ \begin{array}{rr}
2 & -1\\
3 & -2 \\
-5 & 7 \\
\end{array} \right]
\hspace{.5in}
C= \left[ \begin{array}{rrr}
1 & 0 & -7\\
4 & 6 & -2\\
-7 & 0 & 1 \\
\end{array} \right]
\]
\begin{enumerate}
\item $2A-3B$
\item  $AB$
\item  $BA$
\item $BC$ 
\end{enumerate}

\item  Given the matrix $B$ below, find $B^{-1}$.
\[
\left[ \begin{array}{rrr}
7 & 11 & 3 \\
5 & 8 & 2 \\
1 & 2 & 1
\end{array} \right]
\]

\item  Are the two matrices below inverses?
Explain why or why not.  A simple yes or no (even if correct) is not worth anything.
Hint: Try not to make this harder then it needs to be.
\[
\left[ \begin{array}{rrr}
1 & 1 & 2 \\
2 & 1 & 1 \\
2 & 2 & 1
\end{array} \right]
\hspace{.5in}
\left[ \begin{array}{rrr}
-1/3 & 1 & -1/3 \\
0 & -1 & 1 \\
2/3 & 0 & -1/2 
\end{array} \right]
\]

\item  Given the fact that the two matrices below are inverses, 
solve the below system of equations \underline{using} inverse matrices.
\[
A=\left[ \begin{array}{rrr}
2 & -1 & -2 \\
3 & -1 & 1 \\
1 & 1 & -1
\end{array} \right]
\hspace{.5in}
A^{-1}=\left[ \begin{array}{rrr}
0 &  1/4 & 1/4 \\
-1/3 & 0 & 2/3 \\
-1/3 & 1/4 & -1/12 
\end{array} \right]
\]
\[
\begin{array}{rrrrrrr}
2x & - & y & - & 2z & = & 7 \\
3x & - & y & + & z & = & 5 \\
x & + & y & - & z & = & -2 \\
\end{array}
\]

\item  Graph the solution to the inequalities and find all the corners 
of the shaded region.
\begin{eqnarray*}
y - 2x & \geq & 0 \\
y + x & \geq & 3 \\
y & \leq & 10 
\end{eqnarray*}


\end{enumerate}


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