ࡱ> { FbjbjBrBr ~  K66$pfggg$F)!ggggg)Jgdg3԰,`0(ggggggg))gggggggggggggggg6 V: 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?   a.c.b.d. ____ 2. Which matrix is not in row-echelon form? a.c.b.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.c.b.no solutiond. Precalculus: Chapter 8 Review Team #: ________ (NON-CALCULATOR) Period: ________ ____ 6. What is the determinant of ? a.-8c.12b.8d.20 ____ 7. Find DE if  and . a.c.b.d. ____ 8. Find the inverse of , if it exists. a.does not existc.b.d. ____ 9. What is B if  and . a.c.b.d. Precalculus: Chapter 8 Review Team #: ________ (CALCULATOR) Period: ________ ____ 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)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 = 7c.infinite solutionsb.x = 7, y = 6, z = 10d.no solution ____ 13. What is the determinant of ? a.-151c.141b.-141d.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)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 = 10c.x = 5, y = 3, and z = 1b.x = 5, y = 8, and z = 0d.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  and  are inverse matrices. a.Yesb.No ____ 18. Solve the matrix equation by using inverse matrices.  a.(, )c.(2, )b.(, 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.c.no solutionb.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 PTS: 1 2. ANS: D PTS: 1 3. ANS: C FeedbackAThere is a column of constant terms.BCCorrect!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 NOT: Example 3: Identify an Augmented Matrix in Row-Echelon Form 4. ANS: D PTS: 1 5. ANS: C FeedbackASubstitute x = 9 and y = 1 back into each equation in the system.BThe system has a unique solution.CCorrect!DSubstitute 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 FeedbackACheck the steps of the Gaussian elimination.BCheck the steps of the Gaussian elimination.CCheck the steps of the Gaussian elimination.DCorrect! 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 FeedbackACorrect!BCheck the steps of the Gauss-Jordan elimination.CCheck the steps of the Gauss-Jordan elimination.DCheck 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 FeedbackACheck the steps of the Gauss-Jordan elimination.BCheck the steps of the Gauss-Jordan elimination.CCheck the steps of the Gauss-Jordan elimination.DCorrect! 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 FeedbackACorrect!BSubstitute x = 5, y = 10, and z = 8 back into each equation in the system.CThe system has a unique solution.DSubstitute 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:  PTS: 1 21. ANS:  PTS: 1 22. ANS:  PTS: 1 23. ANS: 3 PTS: 1 24. 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