A-50 Answers to Selected Exercises 61. c 3 + 424 2215 + 1226 -322 -2230 d 63. The product cannot be calculated. 65. 32 7 -44 67. £ -15 -1 7 -16 0 6 3 9 12§ 69. £ 23 -6 33 -9 -2 1§ 71. £ -25 0 -15 23 -6 33 11 -12 45§ 73. The product cannot be calculated. 75. c 10 15 -10 -5d 77. BA≠AB, BC≠CB, AC≠CA 79. (a) c 38 -7 -8 -2d (b) c 18 19 24 18d 81. (a) £ 0 0 0 1 1 0 -1 0 1§ (b) £ 0 0 0 1 1 0 -1 0 1§ 83. 1 85. (a) £ 50 10 60 100 90 120 30 50 40§ (b) £ 12 10 15§ (c) £ 2050 1770 2520§ (d) $6340 87. Answers will vary a little if intermediate steps are rounded. (a) 2940, 2909, 2861, 2814, 2767 (b) The northern spotted owl will become extinct. (c) 3023, 3051, 3079, 3107, 3135 9.8 Exercises 1. c 6 4 -1 8d 3. c 1 0 0 1d , or I2 5. c 3 -6 -1 3d 9. yes 11. no 13. no 15. yes 17. c - 1 5 2 5 - 2 5 - 1 5d 19. c 2 - 3 2 1 - 1 2d 21. The inverse does not exist. 23. £ -1 0 2 1 -1 -1 1 0 -1§ 25. ≥ 7 8 - 1 8 - 1 8 - 3 8 5 8 - 3 8 - 3 8 - 3 8 5 8¥ 27. ≥ - 15 4 5 4 - 3 2 - 1 4 1 4 0 -3 1 -1¥ 29. E 1 2 1 10 - 7 10 1 5 0 - 2 5 4 5 1 5 1 2 3 10 - 11 10 - 2 5 -1 - 1 5 12 5 3 5U 31. E 0 1 3 2 3 - 1 3 - 1 3 2 3 1 1 3 1 3 - 1 3 - 4 3 1 3 2 3 -1 - 4 3 0U 33. 512, 326 35. 51-2, 426 37. E A -2, 3 4B F 39. E A - 1 2 , 2 3B F 41. 514, -926 43. E A6, - 5 6B F 45. The inverse of c 7 14 -2 -4d does not exist. 47. 513, 1, 226 49. E A5 4 , 1 4 , - 3 4B F 51. 5111, -1, 226 53. 511, 0, 2, 126 55. (a) 602.7 = a + 5.543b + 37.14c 656.7 = a + 6.933b + 41.30c 778.5 = a + 7.638b + 45.62c (b) a = -490.5, b = -89, c = 42.72 (c) S = -490.5 - 89A + 42.72B (d) S = 843.6 (e) S = 1547.6; Predictions made beyond the scope of the data are valid only if current trends continue. 57. Answers will vary. 59. c -0.1215875322 1.544369078 0.0491390161 -0.046799063d 61. £ 2 -4 3 -2 0 3 0 4 -3§ 63. 511.68717058, -1.30699024226 65. 5113.58736702, 3.929011993, -5.34278007626 73. A-1 = A2 = £ 1 0 0 0 -1 1 0 -1 0§ Chapter 9 Review Exercises 1. 510, 126 3. 51-5y + 9, y26; infinitely many solutions 5. ∅; inconsistent system 7. E A1 3 , 1 2B F 9. 513, 2, 126 11. 515, -1, 026 13. One possible answer is x + y = 2 x + y = 3. 15. rice: 1 3 cup; soybeans: 1 5 cup 17. 5 blankets; 3 rugs; 8 skirts 19. (a) q 0 (36, 54) p = q p 36 54 81 108 p = 81 – q 3 2 3 4 (b) 36 (c) $54 21. y1 = 12 5 x 2 - 31 5 x + 3 2 , or y1 = 2.4x 2 - 6.2x + 1.5 23. 51x, -2x + 1, -11x + 626 25. 51-2, 026 27. 51-3, 226 29. 510, 3, 326 31. 10 lb of $4.60 tea; 8 lb of $5.75 tea; 2 lb of $6.50 tea 33. 1982; 191 thousand master’s degrees 35. -25 37. 0 39. -1 41. 51-4, 226 43. Cramer’s rule does not apply because D= 0; ∅ 45. 5114, -15, 3526 47. E 8 19F 49. 2 x - 1 - 6 3x - 2 51. 1 x - 1 - x + 3 x2 + 2 53. 51-3, 42, 11, 1226 55. 51-4, 12, 1-4, -12, 14, -12, 14, 126 57. E15, -22, A -4, 5 2B F 59. 51-2, 02, 11, 126
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