PART I-MULTIPLE CHOICE
Each problem is worth 4 points.
1. For which of the following matrices is
A ( B + C ) dened?
(a)
A
,
B
, and
C are all 3x2
(b)
A is 3x2 and
B and
C are 2x3
(c) A and C are 3x2 and B is 2x3
(d) A is 3x2, B is 3x3, and C is 2x3
(e)
A and
B are 3x2 and
C is 2x3
2. For which of the following matrices is
A + ( B T + C ) dened?
(a)
A
,
B
, and
C are all 3x2
(b)
A is 3x2 and
B and
C are 2x3
(c)
A and
C are 3x2 and
B is 2x3
(d)
A is 3x2,
B is 3x3, and
C is 2x3
(e)
A and
B are 3x2 and
C is 2x3
3. For the matrices below, if C = AB , what is C
56
 1 0 − 1 
?
0
A =









2
− 1
1
0
1 − 2
− 1
1
1
2 −
2
0
1
2






,
B =





−
0
1
2
− 3
3
3
−
−
0
3
2
1
0
1
−
2
2
0
−
−
1
2
0
−
1
1
2
1 2 − 1


(a) − 1
(b)
0
(c)
1
(d) − 2
(e)
AB is not possible
1

4. The row-reduced Gauss-Jordan matrix for a system of equations is given below. Which of the following statements is true about the solution to the original system of equations



 x y z
1 0 0 3
0 1 0 1
0 0 1 0
0 0 0 0




I. There is no solution since
1 = 0
II. There are an innite number of solutions
III.
x = 3 , y = 1 , z = 0 is a solution
(a) None of the three are true.
(b) I only
(c) II only
(d) III only
(e) II and III only
5. Which matrix product below gives the solution to the following system of equations:
.
(a)


1 1 − 3
2 5 1
1 3 2
 
 
8
− 5
0


(b)


7 − 11 16
− 3 5 − 7
1 − 2 3
 
 
8
− 5
0


(c) 8 − 5 0


1 1 − 3
2 5 1
1 3 2


(d)
8 − 5 0


7 − 11 16
− 3 5 − 7
1 − 2 3


(e)


1 1 − 3
2 5
8
1 − 5
1 3 2 0
 
  x y z

 x + y − 3 z = 8
2 x + 5 y + z = − 5 x + 3 y + 2 z = 0
2

 2 − 1 0 0
6. Given the augmented matrix row operations:
R
2
↔ R
1
, R
2

1 0 1 5
−
0 2 − 1 20
2 R
1
→ R
2
.


, which matrix is the result of the following
(a)


1 0 1 5
0 − 1 − 2 − 10
0 2 − 1 20


(b)


− 2 0 − 2 − 10
0 − 1 − 2 − 10
0 2 − 1 20


(c)


0 − 1 − 2 − 10
1 0 1 5
0 2 − 1 20


(d)


1 0 1 5
− 3 2 1 5
0 2 − 1 20


(e)


1 0 0 5
0 1 0 10
0 0 1 0


7. Which of the following is the inverse of
A =
0 a b 0
?
(a)
(b)
(c)
0 − 1 b
− 1 a
0
0
1 b
0
− 1 b
−
0
1 a
1 a
0
(d)
0
1 a
1 b
0
(e) The matrix
A is singular
8. $6,400 is borrowed at 6% annual simple interest. What is the amount due at the end of 3 months?
(a) $1,152
(b) $7,552
(c) $7,622.50
(d) $96
(e) $6,496
3

9. Based on life expectancy statistics, you anticipate living another 17 years after you retire. If you want to draw a $10,000/month salary throughout that time, how much money should you have saved in an IRA earning 3% per year compounded monthly when you retire (to the nearest dollar)?
(a)
$1 , 596 , 488
(b)
$1 , 225 , 791
(c)
$612 , 000
(d)
$2 , 656 , 927
(e) $1 , 997 , 078
10. You wish to deposit money in a 4-year CD. Which rate will give you the highest return?
(a) 5% per year compounded quarterly
(b) 5% per year compounded monthly
(c) 5% per year compounded daily (assume 360)
(d) 5.1% per year compounded daily (assume 360)
(e) 5.25% per year compounded annually
11. You set aside $100 per month into a mutual fund which earns 6% per year compounded monthly.
How much interest has the account earned after 10 years?
(a) $2,992.65
(b) $3,816.95
(c) $4,387.93
(d) $7,200.00
(e) $9,490.17
12. For the matrices below, if
C = AB
, what is
C
23
 x 0 − 1   0 − 3 0 1
?

A =

2 1 0

,
B =

− 1 z − 3 0

− 1 0 y 2 3 − 2 1
(a) − 3
(b)
3 + 3 y
(c)
0
(d) 3 + z + 3 y
(e) AB is not possible
4


13. Given the augmented matrix

2 − 1 0 0
1 0 1 5
0 2 − 1 20


, which series of row operations give the desired rst column (1 and 0's)
(a)
R
1
× (1 / 2) , R
2
− 1 → R
2
(b) R
1
↔ R
3
, R
3
− 2 R
2
→ R
3
(c) R
1
(d)
R
1
↔ R
2
, R
2
× R
3
× ( − 1 / 2) , R
2
+ R
1
(e)
R
1
↔ R
2
, R
2
− 2 R
1
→ R
2
→ R
2
.
14. $2,000 is invested at simple interest and after 9 months the account has a value of $2,090. What is the interest rate?
(a)
0 .
005%
(b)
0 .
06%
(c)
0 .
5%
(d)
5 .
88%
(e) 6%
15. Find the amount of time (rounded to two decimal places) for an account earning interest compounded quarterly at a rate of 5.8% per year to grow from $3000 to $5000.
(a) 35.48 years
(b) 9.06 years
(c) 8.83 years
(d) 8.87 years
(e) 28.74 years
Part II
16. You buy a house for $150,000 and put 10% down. You nance the rest at 4 .
75% per year compounded monthly for 30 years.
(a) What are your monthly payments?
(b) How much do you pay total on the house?
(c) What is the equity in the house after 20 years?
5

17. You begin working when you turn 22 with a monthly salary of $4,500.
(a) Assuming ination runs at 2% per year, what will your monthly salary be when you turn
70 (in 48 years)?
(b) You estimate that you need $1,600,000 in your IRA when you retire to live on the salary from part (a) for the rest of your life. To achieve that goal, how much do you have to deposit every month while you are working into the IRA if it earns 8% per year compounded monthly?
18. You buy a new car by making a $4000 down payment and nancing the remaining balance by taking out a 3-year loan. You agree to pay $570 per month at 3.9% per year compounded monthly to pay o the car.
(a) What is the original cash price of the car?
(b) Complete the amortization table below.
Period Payment Interest paid Principal paid Outstanding Balance
0
1
2
X X X
6

19. You wish to save up $6,250 to buy a car in 3 years, and have found a stock that has historically earned a 5.5% return per year compounded monthly.
(a) How much do you need to set aside each month in order to achieve your goal?
(b) How much interest do you earn during those three years?
(c) How much interest do you earn during the third month of the second year?
20. Write a system of equations to model the following. DO NOT SOLVE YOUR SYSTEM.
Aggie Living, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units, two-bedroom townhouses, and three-bedroom townhouses. A total of 169 units is planned. One-bedroom units will be 600 square feet, two-bedroom townhouses will be
900 square feet, and three-bedroom townhouses will be 1100 square feet. The entire complex will have a total of 132,500 square feet of living space. If they want to build three times as many one-bedroom units as three-bedroom townhouses, how many units of each type will be in the complex?
7

21. Find the values of x, y, and z which make the following equation true:


1 8
3 10 x − 5
 

− 3
 y
1
8
4
8 2 z + 1
 

= 2

− 4 − 8
0 − 1
4 x


22. Matrix
A represents the number of servings of each food that each person eats in a given day.
Matrix
B represents the number of units of each nutrient per serving of each food:
A =
Chris
Sam
Shel



 chicken carrots pasta
2 1 0 .
5
2 0 .
5 0 .
5
0 2 2




B = chicken carrots pasta




Zinc Vit A Vit B1
14 14 12
2
0
10
8
8
8




(a) Find
AB
(using any method)
(b) Interpret the meaning of the entry in the 2nd row, 3rd column of
AB
.
8

23. For the row-reduced matrix below, x represents the amount of money invested at 5%, y represents the amount of money invested at 6%, and z represents the amount of money invested at 7% (all in dollars). Give the general solution of the system corresponding to this matrix, then determine the largest and smallest possible values of the free variable and tell how much money is invested at each percentage for both.
 1 0 − 1 600 

0 1
0 0
2
0
7400
0

24. Let
A = x −
− 2 7
3 and
B =
I or explain why it is not possible.
1 − y − 1 2
1
. Find the values of x and y which make
A − 3 B =
9