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Practice and Applications

7. $a = 2, b = - 3$ $a = 2, b = - 3$
9. $x = 2, y = - 3, z = 4, a = 5, b = - 1, c = 6$ $x = 2, y = - 3, z = 4, a = 5, b = - 1, c = 6$
11. $x = - 1, y = \frac{1}{2}, a = - \frac{1}{2}, b = - \frac{3}{2}$ $x = - 1, y = \frac{1}{2}, a = - \frac{1}{2}, b = - \frac{3}{2}$
13. $[\begin{array}{r} 1 & - 3 \\ 8 & - 5 \\ - 8 & - 2 \\ 3 & - 10 \end{array}]$ $[\begin{array}{r} 1 & - 3 \\ 8 & - 5 \\ - 8 & - 2 \\ 3 & - 10 \end{array}]$
15. $[\begin{array}{r} - 3 & 3 \\ 0 & - 7 \\ 2 & - 2 \\ - 1 & - 4 \end{array}]$ $[\begin{array}{r} - 3 & 3 \\ 0 & - 7 \\ 2 & - 2 \\ - 1 & - 4 \end{array}]$
17. $[\begin{array}{r} 7 & - 6 \\ - 4 & 20 \\ - 1 & 6 \\ 1 & 15 \end{array}]$ $[\begin{array}{r} 7 & - 6 \\ - 4 & 20 \\ - 1 & 6 \\ 1 & 15 \end{array}]$
19. $[\begin{array}{r} 0 & 0 \\ 0 & 0 \end{array}]$ $[\begin{array}{r} 0 & 0 \\ 0 & 0 \end{array}]$
21. $[\begin{array}{r} 0.30 & 0.06 & 0 \\ 0.02 & - 0.08 & 0.10 \\ - 0.01 & - 0.17 & 0.20 \end{array}]$ $[\begin{array}{r} 0.30 & 0.06 & 0 \\ 0.02 & - 0.08 & 0.10 \\ - 0.01 & - 0.17 & 0.20 \end{array}]$
23. $[\begin{array}{r} - 2 & \frac{5}{2} \\ - 1 & 1 \end{array}]$ $[\begin{array}{r} - 2 & \frac{5}{2} \\ - 1 & 1 \end{array}]$
25. $[\begin{array}{r} - \frac{7}{6} & \frac{1}{6} \\ - \frac{2}{3} & - \frac{4}{3} \end{array}]$ $[\begin{array}{r} - \frac{7}{6} & \frac{1}{6} \\ - \frac{2}{3} & - \frac{4}{3} \end{array}]$
27. $[\begin{array}{r} 11 & 10 & 3 \\ - 4 & - 4 & - 1 \\ 3 & 3 & 1 \end{array}]$ $[\begin{array}{r} 11 & 10 & 3 \\ - 4 & - 4 & - 1 \\ 3 & 3 & 1 \end{array}]$
29. $[\begin{array}{r} \frac{1}{2} & - \frac{1}{2} & - 1 \\ - 3 & 2 & 1 \\ - 4 & 3 & 2 \end{array}]$ $[\begin{array}{r} \frac{1}{2} & - \frac{1}{2} & - 1 \\ - 3 & 2 & 1 \\ - 4 & 3 & 2 \end{array}]$
31. $x = - 3, y = 1$ $x = - 3, y = 1$
33. $x = 10, y = - 15$ $x = 10, y = - 15$
35. $u = - 1, v = - 3, w = 0$ $u = - 1, v = - 3, w = 0$
37. $x = 1, y = \frac{1}{2}, z = - \frac{1}{3}$ $x = 1, y = \frac{1}{2}, z = - \frac{1}{3}$
39. $x = - 3, y = 1$ $x = - 3, y = 1$
41. $u = - 1, v = - 3, w = 0$ $u = - 1, v = - 3, w = 0$
43. $x = 1, y = \frac{1}{2}, z = - \frac{1}{3}$ $x = 1, y = \frac{1}{2}, z = - \frac{1}{3}$
45. Unlimited number of solutions
47. $u = - 1, v = - 3, w = 0$ $u = - 1, v = - 3, w = 0$
49. $x = 1, y = \frac{1}{2}, z = - \frac{1}{3}$ $x = 1, y = \frac{1}{2}, z = - \frac{1}{3}$
51. $x = 3, y = 1, z = - 1$ $x = 3, y = 1, z = - 1$
53. $x = 1, y = 2, z = - 3, t = 1$ $x = 1, y = 2, z = - 3, t = 1$
55. $x = - \frac{1}{3}, y = 3, z = \frac{2}{3}, t = - 4$ $x = - \frac{1}{3}, y = 3, z = \frac{2}{3}, t = - 4$
57. $r = \frac{1}{2}, s = - 7, t = - \frac{3}{4}, u = 5, v = \frac{3}{2}$ $r = \frac{1}{2}, s = - 7, t = - \frac{3}{4}, u = 5, v = \frac{3}{2}$
59. $[\begin{array}{r} 1 & 0 \\ 15 & 16 \end{array}], [\begin{array}{r} 1 & 0 \\ 63 & 64 \end{array}], [\begin{array}{r} 1 & 0 \\ 255 & 256 \end{array}]$ $[\begin{array}{r} 1 & 0 \\ 15 & 16 \end{array}], [\begin{array}{r} 1 & 0 \\ 63 & 64 \end{array}], [\begin{array}{r} 1 & 0 \\ 255 & 256 \end{array}]$
61. $B^{3} = [\begin{array}{r} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$ $B^{3} = [\begin{array}{r} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$
63. 33
65. 323
67. 33
69. 323
71. $N^{- 1} = - N = [\begin{array}{r} 0 & 1 \\ - 1 & 0 \end{array}]$ $N^{- 1} = - N = [\begin{array}{r} 0 & 1 \\ - 1 & 0 \end{array}]$
73.

$\begin{array}{l} [\begin{array}{c} n & 1 + n \\ 1 - n & - n \end{array}] [\begin{array}{c} n & 1 + n \\ 1 - n & - n \end{array}] \\ = [\begin{array}{c} n^{2} + (1 - n^{2}) & (n + n^{2}) - (n + n^{2}) \\ (n - n^{2}) - (n - n^{2}) & (1 - n^{2}) + n^{2} \end{array}] \\ = [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] \end{array}$ $\begin{array}{l} [\begin{array}{c} n & 1 + n \\ 1 - n & - n \end{array}] [\begin{array}{c} n & 1 + n \\ 1 - n & - n \end{array}] \\ = [\begin{array}{c} n^{2} + (1 - n^{2}) & (n + n^{2}) - (n + n^{2}) \\ (n - n^{2}) - (n - n^{2}) & (1 - n^{2}) + n^{2} \end{array}] \\ = [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] \end{array}$
75. $[\begin{array}{r} 8 & 10 \\ 6 & 8 \end{array}]$ $[\begin{array}{r} 8 & 10 \\ 6 & 8 \end{array}]$
77. $(A + B) (A - B) = [\begin{array}{r} - 6 & 2 \\ 4 & 2 \end{array}], A^{2} - B^{2} = [\begin{array}{r} - 10 & - 4 \\ 8 & 6 \end{array}]$ $(A + B) (A - B) = [\begin{array}{r} - 6 & 2 \\ 4 & 2 \end{array}], A^{2} - B^{2} = [\begin{array}{r} - 10 & - 4 \\ 8 & 6 \end{array}]$
79. $[\begin{array}{r} \frac{1}{2} & \frac{1}{3} \\ 0 & \frac{1}{6} \end{array}] = \frac{1}{2} [\begin{array}{r} 1 & \frac{2}{3} \\ 0 & \frac{1}{3} \end{array}]$ $[\begin{array}{r} \frac{1}{2} & \frac{1}{3} \\ 0 & \frac{1}{6} \end{array}] = \frac{1}{2} [\begin{array}{r} 1 & \frac{2}{3} \\ 0 & \frac{1}{3} \end{array}]$
81. $R_{1} = 4 Ω, R_{2} = 6 Ω$ $R_{1} = 4 Ω, R_{2} = 6 Ω$
83. $F = 303 lb, T = 175 lb$ $F = 303 lb, T = 175 lb$
85. $R_{1} = 4 Ω, R_{2} = 6 Ω$ $R_{1} = 4 Ω, R_{2} = 6 Ω$
87. $F = 303 lb, T = 175 lb$ $F = 303 lb, T = 175 lb$
89. 0.22 h after police pass intersection
91. 30 g, 50 g, 20 g
93.

$\begin{array}{l} [\begin{array}{r} 12, 000 & 24, 000 & 4, 000 \\ 15, 000 & 8, 000 & 30, 000 \end{array}] + [\begin{array}{r} 15, 000 & 12, 000 & 2, 000 \\ 20, 000 & 3, 000 & 22, 000 \end{array}] \\ = [\begin{array}{r} 27, 000 & 36, 000 & 6, 000 \\ 35, 000 & 11, 000 & 52, 000 \end{array}] \end{array}$ $\begin{array}{l} [\begin{array}{r} 12, 000 & 24, 000 & 4, 000 \\ 15, 000 & 8, 000 & 30, 000 \end{array}] + [\begin{array}{r} 15, 000 & 12, 000 & 2, 000 \\ 20, 000 & 3, 000 & 22, 000 \end{array}] \\ = [\begin{array}{r} 27, 000 & 36, 000 & 6, 000 \\ 35, 000 & 11, 000 & 52, 000 \end{array}] \end{array}$
95.

$\begin{array}{l} (R_{1} + R_{2}) i_{1} - R_{2} i_{2} = 6 \\ - R_{2} i_{1} + (R_{1} + R_{2}) i_{2} = 0 \end{array}$ $\begin{array}{l} (R_{1} + R_{2}) i_{1} - R_{2} i_{2} = 6 \\ - R_{2} i_{1} + (R_{1} + R_{2}) i_{2} = 0 \end{array}$

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Table of Contents for Practice and Applications

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Table of Contents for
Practice and Applications