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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