MAT 183 
Spring
2007
Final Exam
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A
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1
LA
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Instructions:
Show all the work you want
graded on this exam. Unsupported answers
may receive little or no credit. List the
values you put into your calculator.
Problem
Points
Score
1
6
2
6
3
5
4
6
5
5
6
6
7
6
8
5
9
6
Total
51
Part
I: Linear Algebra
1.
a.
(2 pts) Find the sum
of
the matrices.
P
6
12
4
~2
7
+
18
5
b.
(4 pts) Suppose
a
and
b
are constants and the inverse
of
the matrix
ax
+
by
+
3z
==
7
Use this to find the solution to the following system
of
equations:
x
+
y
+
5z
==
2
{
2x+
y+9z
=3
1
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2.
Each
of
the following matrices is the matrix of a system
of
linear equations in
x,
y
and
z.
Find all solutions to the system
of
equations in each case.
2
1
0
2 2
a.
(3
pts)
0
1
b.
(3
pis)
~
1 1
4
4
2
1
5
9
~
~
3.
(5 pts) A business has a plastics division and a metal division. For each
$1
worth
of
output,
the plastics division needs 10¢
of
output from the plastics division and 6¢ from the metal
division. For each
$1
worth
of
output, the metal division needs 12¢
of
output from the
plastics division and 14¢ from the metal division. What level
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 Spring '09
 NA
 Probability, pts, Elementary algebra, Plastics Division, picture tubes

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