961 9.7 Properties of Matrices Let A = c -2 0 4 3d and B = c -6 4 2 0d . Find each of the following. See Examples 2 – 4. 41. 2A 45. 2A - 3B 55. c 1 3 2 4d c -1 7d 59. c 22 23 22 227 -218 0d £ 8 9 0 -10 12 2§ 47. -A + 1 2 B 57. c 3 5 -4 0 1 2d £ -1 4 2§ 61. c 23 225 1 322d c 23 423 -26 0 d 63. c -3 4 0 0 2 2 1 6d c -4 0 2 1d 65. 3-2 4 14£ 3 2 0 -2 1 -1 4 0 4§ 42. -3B 46. -2A + 4B 56. c -1 7 5 0d c 6 2d 60. c -9 3 2 0 1 0d C 25 220 -225 S 48. 3 4 A - B 58. c -6 2 3 9 5 1d £ -2 0 3§ 62. c 27 2 0 228d c 223 0 -27 -6 d 64. c -1 0 2 2 4 -3 1 5d c 1 -2 2 5 4 1d 66. 30 3 -44£ -2 0 -1 6 4 1 3 2 4§ Suppose that matrix A has dimension 2 * 3, B has dimension 3 * 5, and C has dimension 5 * 2. Can the given product be calculated? If it can, determine its dimension. See Example 5. 49. AB 50. CA 51. BA 52. AC 53. BC 54. CB Find each product, if possible. See Examples 5–7. 67. £ -2 2 4 -3 -1 -2 -4 0 3§ £ 0 1 3 1 2 2 4 -1 -2§ 68. £ -1 0 0 2 3 1 0 2 4§ £ 2 0 3 -1 2 0 2 1 -1§ Given A = c 4 3 -2 1d , B = £ 5 0 3 1 -2 7§ , and C = c -5 0 4 3 1 6d , find each product, if possible. See Examples 5–7. 43. 3 2 B 44. - 3 2 A 69. BA 70. AC 71. BC 72. CB 73. AB 74. CA 75. A2 76. A3 (Hint: A3 = A2 # A) 77. Concept Check Compare the answers to Exercises 69 and 73, 71 and 72, and 70 and 74. How do they show that matrix multiplication is not commutative? 78. Concept Check Why is it not possible to find C2 for matrix C defined as follows? C = c -5 4 1 0 3 6d
RkJQdWJsaXNoZXIy NjM5ODQ=