A-32 ANSWERS 69. 2 71. 1, 2, 3 73. 0 75. 2 77. a) Tuesday b) Wednesday 79. Knowledge is power 80. 0 SECTION 9.4, PAGE 577 1. Matrix 3. 2 5. Dimensions 7. Columns, rows 9. ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1 4 5 5 11. − ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ 2 5 5 4 8 6 13. − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1 9 6 8 15. − ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ 1 9 18 17 2 2 17. ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 9 6 15 0 19. ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 0 13 22 0 21. ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 26 18 48 24 23. ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 15 22 25. [ ] 13 2 27. + = − − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ × = − − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B A B 1 5 6 7 ; 32 15 24 12 29. + = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B 8 1 3 4 3 0 ; cannot be multiplied 31. Cannot be added; × = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B 24 34 24 34 33. Cannot be added; cannot be multiplied 35. + = + = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B B A 7 2 6 1 37. + = + = − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B B A 8 0 6 8 39. + + = + + = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B C A B C ( ) ( ) 7 13 2 10 41. + + = + + = − ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ A B C A B C ( ) ( ) 4 14 3 15 8 1 43. No 45. Yes 47. × × = × × = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B C A B C ( ) ( ) 41 13 56 16 49. × × = × × = − − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ A B C A B C ( ) ( ) 16 10 24 2 51. 158 280 95 215 362 94 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 69. a) * R S T U V I R V T U S I R S U I V R T S T S R I V U T U T V R I S U V I U S T R V I R S T U V I b) Yes. It is closed; identity element is I; inverses R V– , SSTTUUVRII – , – , – , – , – ; and the associative property will hold. c) No, it is not commutative. For example, R S S R * * . ≠ 70. a) Yes b) Yes, 1 c) Yes, 1 d) Yes e) Yes f) Yes SECTION 9.3, PAGE 566 1. − m 1 3. Modular 5. Congruent 7. 0 9. 4 11. 2 13. 1 15. 2 17. 1 19. 5 21. 5 23. 6 25. 5 27. 4 29. 3 31. 5 33. 5 35. { } 37. 6 39. 2 41. Sunday 43. Thursday 45. Sunday 47. Friday 49. August 51. August 53. September 55. July 57. a) 1792, 1796, 1800, 1804, 1808 b) 2024, 2028, 2032, 2036, 2040 c) 2552, 2556, 2560, 2564, 2568, 2572 59. a) Working at Longboat Key b) Resting c) Working at The Meadows 61. a) 5 b) No c) 54 weeks from this week 63. a) 3 p.m.–11 p.m. b) 7 a.m.–3 p.m. c) 7 a.m.–3 p.m. 65. a) + 0 1 2 0 0 1 2 1 1 2 0 2 2 0 1 b) Yes c) Yes, 0 d) Yes; 0–0, 1–2, 2–1 e) + + = + + (12)2 1(22) f) Yes; + = + 2 1 1 2 g) Yes h) Yes 67. a) × 0 1 2 3 0 0 0 0 0 1 0 1 2 3 2 0 2 0 2 3 0 3 2 1 b) Yes c) Yes, 1 d) No; no inverse for 0 or for 2, inverse of 1 is 1, inverse of 3 is 3 e) × × = × × (12)3 1(23) f) Yes; × = × 2 3 3 2 g) No; 0 and 2 do not have an inverse. Student Adult Senior citizen Matinee Evening 53. 38 50 56 72 17 26 10 14 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ Large Small Sugar Flour Milk Eggs
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