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Precalculus: Chapter 8 Review
(NON-CALCULATOR)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Team #:
Period:
________
________
Write the letter for the correct answer in the blank at the right of each question.
____
____
1. What is the augmented matrix for the given system?
a.
c.
b.
d.
2. Which matrix is not in row-echelon form?
a.
b.
c.
d.
____
3. Choose the phrase that best describes the matrix.
____
a.
c.
b.
d. none of the above
4. Solve the system of equations using a matrix and Gaussian elimination.
____
a. (4, 2)
c. (4, -2)
b. (-4, -2)
d. (-4, 2)
5. Solve the following system of equations using an inverse matrix.
4x + 5y = –21
–2x – 4y = 6
a.
b. no solution
c.
d.
Precalculus: Chapter 8 Review
Team #:
Period:
(NON-CALCULATOR)
____
6. What is the determinant of
?
a. -8
b. 8
____
____
____
c. 12
d. 20
7. Find DE if
and
.
a.
c.
b.
d.
8. Find the inverse of
, if it exists.
a. does not exist
c.
b.
d.
9. What is B if
and
.
a.
c.
b.
d.
________
________
Precalculus: Chapter 8 Review
Team #:
Period:
(CALCULATOR)
________
________
____ 10. Write a matrix equation for the given systems of equations.
a.
c.
b.
d.
____ 11. Solve the following system of equations using an inverse matrix.
a. (1, 0, -2)
b. (-1, 0, -2)
c. (-1, 0, 2)
d. (1, 0, 2)
____ 12. Solve the system of equations.
10x + 24y + 2z = –18
–2x – 7y + 4z = 6
–14x – 48y + 26z = 42
a. x = –8, y = 2, z = 7
b. x = 7, y = 6, z = –10
____ 13. What is the determinant of
a. -151
b. -141
c. infinite solutions
d. no solution
?
c. 141
d. 151
____ 14. FOOD The table shows several boxes of assorted candy available at a candy shop. What is the price per
pound for each candy?
a. ($0.85, $0.75, $0.80)
b. ($0.75, $0.80, $0.85)
c. ($0.80, $0.75, $0.85)
d. ($0.75, $0.85, $0.80)
Precalculus: Chapter 8 Review
Team #:
Period:
(CALCULATOR)
________
________
____ 15. Solve the system of equations using a matrix and Gauss-Jordan elimination.
2x – 3y + z = –14
14x – 18y + 12z = –30
–15x + 21y – 9z = 81
a. x = –3, y = 6, and z = 10
b. x = 5, y = 8, and z = 0
c. x = –5, y = –3, and z = –1
d. no solution
____ 16. Solve the system of equations.
2x – 2y + 6z – 26w = 30
–2x + y – 6z + 21w = –33
3x – 3y + 6z – 21w = 21
a. (–6 + 8w, 3 – 3w, 9 – w, w)
b. (–1 + 5w, 6 + 4w, –7 – 8w, w)
____ 17. Determine whether
a. Yes
c. (6, 113, 6, –8)
d. (–6 – 10w, 3 – 5w, 8 + 6w, w)
and
are inverse matrices.
b. No
____ 18. Solve the matrix equation by using inverse matrices.
a.
3
( , 12)
2
b. (8, 5)
c. (–2, 1)
d. (–2, 5)
____ 19. Use an inverse matrix to solve the system of equations, if possible.
5x + 4y + z = –73
3x – 6y + 3z = 45
–4x + 8y – z = –33
a.
b.
c. no solution
d.
Precalculus: Chapter 8 Review
Team #:
Period:
________
________
Short Answer
20. If
, find
.
21. If A and B are inverse 2 x 2 matrices, what matrix represents the product of A and B?
22. What is the inverse of matrix A, if
?
23. Find the determinant of
using minor and cofactors.
24. Find the determinant of
using minor and cofactors.
25. Find the inverse of
, if it exists. Use both calculator and non-calculator approaches.
Precalculus: Chapter 8 Test Review
Answer Section
MULTIPLE CHOICE
1. ANS: C
2. ANS: D
3. ANS: C
PTS: 1
PTS: 1
Feedback
A
B
There is a column of constant terms.
C
D
Correct!
PTS:
OBJ:
NAT:
NOT:
4. ANS:
5. ANS:
1
DIF: Average
REF: Lesson 6-1
6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
2
STA: 8.D.5
TOP: Multivariable Linear Systems and Row Operations
Example 3: Identify an Augmented Matrix in Row-Echelon Form
D
PTS: 1
C
Feedback
A
B
C
D
6.
7.
8.
9.
10.
11.
12.
Substitute x = –9 and y = –1 back into each equation in the system.
The system has a unique solution.
Correct!
Substitute x = –4 and y = –1 back into each equation in the system.
PTS:
OBJ:
NAT:
KEY:
NOT:
ANS:
ANS:
ANS:
ANS:
ANS:
OBJ:
NAT:
KEY:
NOT:
ANS:
ANS:
1
DIF: Average
REF: Lesson 6-3
6-3.2 Solve systems of linear equations using Cramer's Rule.
2
STA: 8.D.5
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
Matrices | Systems of Linear Equations | Cramer's Rule
Example 3: Use Cramer's Rule to Solve a 2x2 System
B
PTS: 1
A
PTS: 1
B
PTS: 1
B
PTS: 1
D
PTS: 1
DIF: Average
REF: Lesson 6-1
6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
2
STA: 8.D.5
TOP: Multivariable Linear Systems and Row Operations
Matrix Equations | Systems of Equations
Example 2: Write an Augmented Matrix
C
PTS: 1
D
Feedback
A
B
C
D
Check the steps of the Gaussian elimination.
Check the steps of the Gaussian elimination.
Check the steps of the Gaussian elimination.
Correct!
PTS:
OBJ:
NAT:
NOT:
13. ANS:
14. ANS:
15. ANS:
1
DIF: Advanced
REF: Lesson 6-1
6-1.2 Solve systems of linear equations using matrices and Gauss-Jordan elimination.
2
STA: 8.D.5
TOP: Multivariable Linear Systems and Row Operations
Example 6: No Solution and Infinitely Many Solutions
C
PTS: 1
A
PTS: 1
A
Feedback
A
B
C
D
Correct!
Check the steps of the Gauss-Jordan elimination.
Check the steps of the Gauss-Jordan elimination.
Check the steps of the Gauss-Jordan elimination.
PTS:
OBJ:
NAT:
NOT:
16. ANS:
1
DIF: Advanced
REF: Lesson 6-1
6-1.2 Solve systems of linear equations using matrices and Gauss-Jordan elimination.
2
STA: 8.D.5
TOP: Multivariable Linear Systems and Row Operations
Example 5: Use Gauss-Jordan Elimination
D
Feedback
A
B
C
D
Check the steps of the Gauss-Jordan elimination.
Check the steps of the Gauss-Jordan elimination.
Check the steps of the Gauss-Jordan elimination.
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 6-1
OBJ: 6-1.2 Solve systems of linear equations using matrices and Gauss-Jordan elimination.
NAT: 2
STA: 8.D.5
TOP: Multivariable Linear Systems and Row Operations
NOT: Example 5: Use Gauss-Jordan Elimination
17. ANS: B
PTS: 1
DIF: Average
REF: Lesson 6-2
OBJ: 6-2.2 Find determinants and inverses of 2x2 and 3x3 matrices.
NAT: 1
STA: 8.C.4b
TOP: Matrix Multiplication, Inverses, and Determinants
KEY: Matrices | Inverses of Matrices
NOT: Example 4: Verify an Inverse Matrix
18. ANS: D
May want to write this as a system of equations, rather than in matrix form. But it still works.
PTS:
OBJ:
NAT:
KEY:
19. ANS:
1
DIF: Advanced
REF: Lesson 6-3
6-3.1 Solve systems of linear equations using inverse matrices.
2
STA: 8.D.5
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
Matrix Equations | Systems of Equations
NOT: Example 1: Multiply Matrices
A
Feedback
A
B
C
D
Correct!
Substitute x = –5, y = –10, and z = –8 back into each equation in the system.
The system has a unique solution.
Substitute x = –5, y = 3, and z = 9 back into each equation in the system.
PTS:
OBJ:
NAT:
KEY:
NOT:
1
DIF: Average
REF: Lesson 6-3
6-3.1 Solve systems of linear equations using inverse matrices.
2
STA: 8.D.5
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
Matrices | Inverse Matrices | Systems of Linear Equations
Example 2: Solve a 3x3 System Using an Inverse Matrix
SHORT ANSWER
20. ANS:
PTS: 1
21. ANS:
PTS: 1
22. ANS:
PTS: 1
23. ANS:
3
PTS: 1
24. ANS:
42
PTS: 1
25. ANS:
PTS: 1