A-28 ANSWERS Chapter 9 SECTION 9.1, PAGE 548 18. (64)16(41) 2 1 6 3 1 3 ? ? − − = − − − = − ≠ SECTION 9.2, PAGE 556 27. + 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 35. + 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 47. Yes; C is the identity element, since the row next to C is identical to the top row, and the column under C is identical to the far-left column. 49. a) The inverse of A is A, since A = A C. b) The inverse of B is B, since B = B C. c) The inverse of C is C, since C = C C. 50. a) A does not have an inverse. b) The inverse of B is B, since ⊗ = B B C. c) The inverse of C is C, since ⊗ = C C C. 55. a) L {4, 5, } b) $ c) Yes d) Yes, L e) Yes, 4–5, 5–4, L L– f) = (4 $ 5) $ 5 4 $ (5 $ 5) g) Yes, = L L $ 4 4 $ h) Yes 56. a) {3, 5, 8, 4} b) t c) Yes d) Yes, 4 e) Yes, 3–8, 5–5, 8–3, 4–4 f) = t t t t (5 8) 4 5 (8 4) g) Yes, = t t 8 3 3 8 h) Yes 60. Not associative: M M M M ; ) ) ( ( ⊗ ⊗ ≠ ⊗ ⊗ not commutative: M M ⊗ ≠ ⊗ 65. a) + E O E E O O O E 66. a) × E O E E E O E O 67. a) It is closed; identity element is 6; inverses: 1–5, 2–2, 3–3, 4–4, 5–1, 6–6; is associative; for example, (2?5)?3 2? (5?3) 3?3 2?2 6 6 ? ? = = = b) 3?1 1?3 2 4 ?= ≠ 48. Euclidean: Given a line and a point not on the line, one and only one line can be drawn parallel to the given line through the given point. Elliptical: Given a line and a point not on the line, no line can be drawn through the given point parallel to the given line. Hyperbolic: Given a line and a point not on the line, two or more lines can be drawn through the given point parallel to the given line. 49. 50. CHAPTER TEST, PAGE 539 14. B9 l C9 D9 A9 A D C B 15. D9 A9 B9 C9 D A B C 16. A9 C9 B9 A C B P 17. D9 C9 B9 A B D C A9 l
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