Dugopolski’s 73College Algebra
Chapter 6 Test — Form A Name:_________________________
Solve each system, using Gaussian elimination.
1. 2.
1. ____________________ 2. ____________________
Let A = , B = , C = , D = , E = , F = ,
2 4 1 0 3 1
1 0 0 1 2 1
3
2 2 0 2
1
and G = . Find each of the following matrices or determinants, if possible.
1 2 3
1 3 0
2 1 1
3. 4. A + B AC
5. 6. G | A |
7. 8. | G | DB
74 Form 6A
9. 10. 2C D FE
Solve each problem.
11. Solve the system using Cramer’s Rule:
11. _____________________
12. Find values of and that make the equation true: = .
2 4 0
1 3 5
12. _____________________
13. Solve the system by using an inverse matrix:
13. _____________________
14. Solve by using a matrix method: One acute angle of a right triangle is 9° less than half the
measure of the other acute angle. What are the measures of the acute angles?
14. _____________________
Dugopolski’s 75College Algebra
Chapter 6 Test — Form B Name: ________________________
Solve each system by using the Gaussian elimination method.
1. 2.
1. ____________________ 2. ____________________
Let A = , B = , C = , D = , E = , F = ,
2 4 1 0 3 1
1 0 0 1 2 1
3
2 2 0 2
1
and G = . Find each of the following matrices or determinants, if possible.
1 2 3
1 3 0
2 1 1
3. 4. A B CA
5. 6. | G | G
7. 8. | A | BD
76 Form 6B
9. 10. C D FE
Solve each problem.
11. Solve the system using Cramer’s Rule:
11. _____________________
12. Find values of and that make the equation true: .
12. _____________________
13. Solve the system by using an inverse matrix:
13. _____________________
14. Solve by using a matrix method: An exit poll of 415 voters found that 40% of the men and
60% of the women were in favor of Proposition D. If 220 voters were in favor of
Proposition D, how many female voters were there?
14. _____________________
Dugopolski’s 77College Algebra
Chapter 6 Test — Form C Name: ________________________
Solve each system by using the Gaussian elimination method.
1. 2.
1. ____________________ 2. ____________________
Let A , B , C , D , E ,
F ,and G = . Find each of the following matrices or
determinants, if possible.
3. 4. A B AC
5. 6. G | B |
7. 8. | G | DB
78 Form 6C
9. 10. 2C D FE
Solve each problem.
11. Solve the system using Cramer’s Rule:
11. _____________________
12. Find values of and that make the equation true: .
12. _____________________
13. Solve the system by using an inverse matrix:
13. _____________________
14. Solve by using a matrix method: Three technology companies spent a total of $15 million
on advertising last year. Companies A and B had combined advertising expenditures of $9
million more than what was spent by Company C. Company A spent $4 million more than
Company B. How much did each company spend on advertising?
14. _____________________
Dugopolski’s 79College Algebra
Chapter 6 Test — Form D Name: ________________________
Solve each system by using the Gaussian elimination method.
1. 2.
1. ____________________ 2. ____________________
Let A , B , C , D , E ,
F ,and G = . Find each of the following matrices or
determinants, if possible.
3. 4. A B CA
5. 6. | G | G
7. 8. | A | BD
80 Form 6D
9. 10. C D FE
Solve each problem.
11. Solve the system using Cramer’s Rule:
11. _____________________
12. Find values of and that make the equation true: .
12. _____________________
13. Solve the system by using an inverse matrix:
13. _____________________
14. Solve by using a matrix method: Mark, Joey, and Tim dined at restaurants a total of 54
times last month. Joey and Tim’s combined restaurant meals totaled one-half of Mark’s. If
Tim dined out 2 fewer times than Joey, then how many times did each dine at restaurants
last month?
14. _____________________
Dugopolski’s 81College Algebra
Chapter 6 Test — Form E Name:_________________________
Multiple Choice: Choose the best answer for each problem.
_____ 1. A matrix has:
a. 3 rows and 2 columns c. 2 rows and 3 columns
b. an order of 6 d. an equivalent 3 2 matrix
_____ 2. The matrix is equivalent to which of the following?
a. c.
b. d.
_____ 3. Use matrices to find the value of such that the graph of
goes through the points , , .
a. c.
b. d.
_____ 4. What is the additive identity for matrices?
a. an zero matrix c. an 1 zero matrix
b. the number zero d. There is none for square matrices.
_____ 5. Perform the indicated operations:
a. b. c. d.
_____ 6. If is a matrix equation for a system of linear equations, and if
is invertible, then the solution to the system is:
a. b. c. d.
82 Form 6E
_____ 7. The matrix equation represents which of the
following?
a. c.
b. d.
_____ 8. If we are able to find the product of two matrices, then the product of
the fourth row of and the fifth column of becomes what entry in the
resultant matrix?
a. The fifth entry on the fourth row c. the fourth entry on the fifth row
b. the fourth entry on the fourth row d. the fifth entry on the fifth row
_____ 9. Let , , .
Which of the following statements is false?
a. c.
b. d.
_____ 10. Let . Find .
a. c.
b. d.
Form 6E 83
_____ 11. Cramer‘s Rule will give the solution for all systems of two linear equations
unless:
a. the coefficient determinant is zero. c. the system has a unique solution.
b. is zero. d. Both and are zero.
_____ 12. Solve using any matrix method: Fifty percent of the male voters and sixty
percent of the female voters supported a recent tax initiative to support first
responders in their region. The tax initiative won by a vote of 3948 “for” to
3236 “against”. How many of the voters were male?
a. 3560 b. 3592 c. 3624 d. 1974
_____ 13. Which of the following statements is false in general for a matrix ?
I. | | is always non-negative.
II. The determinant of can only be found if is a square matrix.
III. To find the determinant of a 3 3 matrix, a sign array is used.
a. I only b. II only c. III only d. I and II
_____ 14. Consider the matrix . What is the minor for ?
a. b. c. d.
_____ 15. What is the determinant of the coefficient matrix for the system:
a. 9 b. 5 c. 0 d. 7
_____ 16. If and , find | | .
a. b. c. d.
84 Dugopolski’s College Algebra
Chapter 6 Test — Form F Name:__________________________________
Multiple Choice: Choose the best answer for each problem.
_____ 1. A matrix has:
a. 2 rows and 3 columns c. 3 rows and 2 columns
b. an order of 6 d. an equivalent 3 2 matrix
_____ 2. The matrix is equivalent to which of the following?
a. c.
b. d.
_____ 3. Use matrices to find the value such that the graph of
goes through the points , , .
a. c.
b. d.
_____ 4. What is the additive identity for matrices?
a. an zero matrix c. an zero matrix
b. the number zero d. There is none for square matrices.
_____ 5. Perform the indicated operations:
a. b. c. d.
_____ 6. If is a matrix equation for a system of linear equations, and if
is invertible, then the solution to the system is:
a. b. c. d.
Form 6F 85
_____ 7. The matrix equation represents which of the
following?
a. c.
b. d.
_____ 8. If we are able to find the product of two matrices, then the product of
the fifth row of and the fourth column of becomes what entry in the
resultant matrix?
a. The fifth entry on the fourth row c. the fourth entry on the fifth row
b. the fourth entry on the fourth row d. the fifth entry on the fifth row
_____ 9. Let , , .
Which of the following statements is false?
a. c.
b. d.
_____ 10. Let . Find .
a. c.
b. d.
86 Form 6F
_____ 11. Cramer‘s Rule will give the solution for all systems of two linear equations
unless:
a. the system has a unique solution. c. the coefficient determinant is zero.
b. is zero. d. Both and are zero.
_____ 12. Solve using any matrix method: Fifty percent of the boys and sixty percent of
the girls who attend Rothschild High School went to a recent pep-rally. The
total number of students at the pep-rally was 320. If there are 590 students
who attend Rothschild High, how many of these students are boys?
a. 250 b. 340 c. 324 d. 430
_____ 13. Which of the following statements is false in general for a matrix ?
I. | | is always non-negative.
II. The determinant of can only be found if is a square matrix.
III. To find the determinant of a 3 3 matrix, a sign array is used.
a. I only b. II only c. III only d. I and II
_____ 14. Consider the matrix . What is the minor for ?
a. b. c. d.
_____ 15. What is the determinant of the coefficient matrix for the system:
a. 9 b. 5 c. 5 d. 7
_____ 16. If and , find | | .
a. b. c. d.
Dugopolski’s 123College Algebra
Chapter Test Keys
CHAPTER 6
124 Chapter 6 Test Key