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Precalculus: Chapter 8 Review Team #: ________
(NON-CALCULATOR) Period: ________
Multiple Choice
Identify the choice that best completes the statement or answers the question.
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?
[pic] [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 2. Which matrix is not in row-echelon form?
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 3. Choose the phrase that best describes the matrix.
[pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |none of the above |
____ 4. Solve the system of equations using a matrix and Gaussian elimination.
[pic]
|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. |[pic] |c. |[pic] |
|b. |no solution |d. |[pic] |
Precalculus: Chapter 8 Review Team #: ________
(NON-CALCULATOR) Period: ________
____ 6. What is the determinant of [pic]?
|a. |-8 |c. |12 |
|b. |8 |d. |20 |
____ 7. Find DE if [pic] and [pic].
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 8. Find the inverse of [pic], if it exists.
|a. |does not exist |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 9. What is B if [pic] and [pic].
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Precalculus: Chapter 8 Review Team #: ________
(CALCULATOR) Period: ________
____ 10. Write a matrix equation for the given systems of equations.
[pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 11. Solve the following system of equations using an inverse matrix.
[pic]
|a. |(1, 0, -2) |c. |(-1, 0, 2) |
|b. |(-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 |c. |infinite solutions |
|b. |x = 7, y = 6, z = –10 |d. |no solution |
____ 13. What is the determinant of [pic]?
|a. |-151 |c. |141 |
|b. |-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?
[pic]
|a. |($0.85, $0.75, $0.80) |c. |($0.80, $0.75, $0.85) |
|b. |($0.75, $0.80, $0.85) |d. |($0.75, $0.85, $0.80) |
Precalculus: Chapter 8 Review Team #: ________
(CALCULATOR) Period: ________
____ 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 |c. |x = –5, y = –3, and z = –1 |
|b. |x = 5, y = 8, and z = 0 |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) |c. |(6, 113, 6, –8) |
|b. |(–1 + 5w, 6 + 4w, –7 – 8w, w) |d. |(–6 – 10w, 3 – 5w, 8 + 6w, w) |
____ 17. Determine whether [pic] and [pic] are inverse matrices.
|a. |Yes |b. |No |
____ 18. Solve the matrix equation by using inverse matrices.
[pic]
|a. |([pic], [pic]) |c. |(–2, [pic]) |
|b. |([pic], 5) |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. |[pic] |c. |no solution |
|b. |[pic] |d. |[pic] |
Precalculus: Chapter 8 Review Team #: ________
Period: ________
Short Answer
20. If [pic], find [pic].
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 [pic]?
23. Find the determinant of [pic] using minor and cofactors.
24. Find the determinant of [pic]using minor and cofactors.
25. Find the inverse of [pic], if it exists. Use both calculator and non-calculator approaches.
Precalculus: Chapter 8 Test Review
Answer Section
MULTIPLE CHOICE
1. ANS: C PTS: 1
2. ANS: D PTS: 1
3. ANS: C
| |Feedback |
|A |There is a column of constant terms. |
|B |[pic][pic] |
|C |Correct! |
|D |[pic][pic] |
PTS: 1 DIF: Average REF: Lesson 6-1
OBJ: 6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
NAT: 2 STA: 8.D.5 TOP: Multivariable Linear Systems and Row Operations
NOT: Example 3: Identify an Augmented Matrix in Row-Echelon Form
4. ANS: D PTS: 1
5. ANS: C
| |Feedback |
|A |Substitute x = –9 and y = –1 back into each equation in the system. |
|B |The system has a unique solution. |
|C |Correct! |
|D |Substitute x = –4 and y = –1 back into each equation in the system. |
PTS: 1 DIF: Average REF: Lesson 6-3
OBJ: 6-3.2 Solve systems of linear equations using Cramer's Rule.
NAT: 2 STA: 8.D.5 TOP: Solving Linear Systems Using Inverses and Cramer's Rule
KEY: Matrices | Systems of Linear Equations | Cramer's Rule
NOT: Example 3: Use Cramer's Rule to Solve a 2x2 System
6. ANS: B PTS: 1
7. ANS: A PTS: 1
8. ANS: B PTS: 1
9. ANS: B PTS: 1
10. ANS: D PTS: 1 DIF: Average REF: Lesson 6-1
OBJ: 6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
NAT: 2 STA: 8.D.5 TOP: Multivariable Linear Systems and Row Operations
KEY: Matrix Equations | Systems of Equations
NOT: Example 2: Write an Augmented Matrix
11. ANS: C PTS: 1
12. ANS: D
| |Feedback |
|A |Check the steps of the Gaussian elimination. |
|B |Check the steps of the Gaussian elimination. |
|C |Check the steps of the Gaussian elimination. |
|D |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 6: No Solution and Infinitely Many Solutions
13. ANS: C PTS: 1
14. ANS: A PTS: 1
15. ANS: A
| |Feedback |
|A |Correct! |
|B |Check the steps of the Gauss-Jordan elimination. |
|C |Check the steps of the Gauss-Jordan elimination. |
|D |Check the steps of the Gauss-Jordan elimination. |
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
16. ANS: D
| |Feedback |
|A |Check the steps of the Gauss-Jordan elimination. |
|B |Check the steps of the Gauss-Jordan elimination. |
|C |Check the steps of the Gauss-Jordan elimination. |
|D |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: 1 DIF: Advanced REF: Lesson 6-3
OBJ: 6-3.1 Solve systems of linear equations using inverse matrices.
NAT: 2 STA: 8.D.5 TOP: Solving Linear Systems Using Inverses and Cramer's Rule
KEY: Matrix Equations | Systems of Equations NOT: Example 1: Multiply Matrices
19. ANS: A
| |Feedback |
|A |Correct! |
|B |Substitute x = –5, y = –10, and z = –8 back into each equation in the system. |
|C |The system has a unique solution. |
|D |Substitute x = –5, y = 3, and z = 9 back into each equation in the system. |
PTS: 1 DIF: Average REF: Lesson 6-3
OBJ: 6-3.1 Solve systems of linear equations using inverse matrices.
NAT: 2 STA: 8.D.5 TOP: Solving Linear Systems Using Inverses and Cramer's Rule
KEY: Matrices | Inverse Matrices | Systems of Linear Equations
NOT: Example 2: Solve a 3x3 System Using an Inverse Matrix
SHORT ANSWER
20. ANS:
[pic]
PTS: 1
21. ANS:
[pic]
PTS: 1
22. ANS:
[pic]
PTS: 1
23. ANS:
3
PTS: 1
24. ANS:
−42
PTS: 1
25. ANS:
[pic]
PTS: 1
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