Test 3
An Aggie does not lie, cheat, or steal, nor tolerate those who do.
April 15, 2015
Last name, First name (print):
Signature:
• There are 11 work out problems on this test.
• You have 75 minutes.
• Show all your work and indicate your final answer clearly. You will be graded not merely on the
final answer, but also on the work leading up to it.
• Calculators are allowed on this test.
• Your calculator’s memory must be cleared before taking the test.
1
1. (12 points) Boris is buying a new car. He investigates car loans and finds three options. For each
loan calculate the total amount Boris must pay back to the lender, and calculate the effective interest
rate for loans b and c.
a) a loan of $15000 to be paid back in one payment after 5 years with a 8.5% simple annual interest
rate,
b) a loan of $15000 to be paid back in one payment after 4 years with a 8.45% annual interest rate
compounded monthly,
c) a loan of $15000 to be paid back in one payment after 10 years with a 8.48% annual interest
rate compounded annually.
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2. (6 points) A fourth lender offers Boris a discounted loan with a simple annual interest rate of 8.4%
on which he pays back $24000 after 6 years. Find the discount and the amount Boris initially receives
with this loan.
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3. (15 points) If Boris accepts a loan of $15000 with a 8.45% annual interest rate compounded monthly,
and agrees to repay the loan in 48 equal monthly payments starting at the end of the first month of
the loan,
a) how much should must each payment be?
b) how much interest is paid over the life of the loan?
c) how much interest is paid in the 5th payment?
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4. (6 points) Squirrel is saving money for a new video game console. If his savings account gives him
5% annual interest compounded monthly, how much should he deposit every month to have $750
saved in 2 years?
5. (12 points) Solve the following systems of equations. If no solutions exist, write “no solution”. If
the system has infinitely many solutions give a parametric solution.
a)
3y − 2z = −11
x + y + 4z = 3
x − 2y + z = 9
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b)
x − 3y + 2z = −7
3x + 4y − 3z = 5
x+y+z =1
x + y − z = −1
c)
x+y+z =1
x−y−z =2
3x + y + z = 4
2y + 2z = −1
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6. (8 points) Find the values of x and y so that
1 1
x
1 -1
y
y
x
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=
1
3
1
-3
.
7. (6 points) Convert the system of equations
4z = 16
3y + 4z = 10
2x + 3y + 4z = 12
into a matrix equation. Solve the matrix equation. If no solutions exist, write “no solution”.
8. (6 points) Patrick owns 3 cats: Daisy, Crazy and Lazy. The following table tells how much wet and
dry food each cat eats in an average day.
wet
dry
Daisy 4 ounces 2 ounces
Crazy 3 ounces 3 ounces
Lazy
6 ounces 4 ounces
The wet food Patrick buys costs $0.25 per ounce and the dry food costs $0.12 per ounce. Write a
product of matrices which calculates how much each cat’s food costs Patrick in an average day.
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9. (16 points) Evaluate the following expressions. If an expression cannot be evaluated, write DNE. In
each expression,
0 1 2
A=
3 4 -5


-1 1
B =  -2 1 
0 3
1 x
C=
0 1
a) AB + C
b) AT B T + C
c) A + B T C
d) B + AT C
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10. (13 points) A particularly lazy and imaginary carpenter builds wooden blocks, chairs and birdhouses.
To do so, he must cut wood, glue the pieces together and paint each block, chair or birdhouse. The
table shows how much time each process takes for each project.
cut glue paint
block
1
0
1
chair
1
2
3
birdhouse
4
4
8
Find how many of each item he can build if he spends exactly 5 hours cutting, 4 hours gluing and 9
hours painting this week. There are multiple valid solutions to this question, find them all.
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11. (5 points) Find A−1 when a> 0 and

0
A= 0
a
0
a+1
a+1
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
a+2
a+2 
a+2
Question
Points
1
12
2
6
3
15
4
6
5
12
6
8
7
6
8
6
9
16
10
13
11
5
Total:
105
Score
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