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Exercises 16.2, page 447

1. $[\begin{array}{r} 5 & 6 & 7 & - 10 \\ - 9 & 0 & - 3 & 12 \\ 1 & 12 & 11 & - 8 \end{array}]$ $[\begin{array}{r} 5 & 6 & 7 & - 10 \\ - 9 & 0 & - 3 & 12 \\ 1 & 12 & 11 & - 8 \end{array}]$
3. $[\begin{array}{r} - 8 & - 12 \end{array}]$ $[\begin{array}{r} - 8 & - 12 \end{array}]$
5. $[\begin{array}{r} 435 \\ 320 \end{array}]$ $[\begin{array}{r} 435 \\ 320 \end{array}]$
7. $[\begin{array}{r} - 10 & \frac{63}{2} \\ - \frac{70}{3} & - 31 \\ 36 & 34 \end{array}]$ $[\begin{array}{r} - 10 & \frac{63}{2} \\ - \frac{70}{3} & - 31 \\ 36 & 34 \end{array}]$
9. $[\begin{array}{r} 33 & - 22 \\ 31 & - 12 \\ 15 & 13 \\ 50 & - 41 \end{array}]$ $[\begin{array}{r} 33 & - 22 \\ 31 & - 12 \\ 15 & 13 \\ 50 & - 41 \end{array}]$
11. $[\begin{array}{r} - 15 & 15 & - 20 \\ 17 & 5 & - 14 \end{array}]$ $[\begin{array}{r} - 15 & 15 & - 20 \\ 17 & 5 & - 14 \end{array}]$
13. $[\begin{array}{r} - 35.78 & 44.28 \\ - 45.28 & 49.49 \end{array}]$ $[\begin{array}{r} - 35.78 & 44.28 \\ - 45.28 & 49.49 \end{array}]$
15. $A B = [\begin{array}{r} 40 \end{array}], B A = [\begin{array}{r} - 1 & 3 & - 8 \\ 5 & - 15 & 40 \\ 7 & - 21 & 56 \end{array}]$ $A B = [\begin{array}{r} 40 \end{array}], B A = [\begin{array}{r} - 1 & 3 & - 8 \\ 5 & - 15 & 40 \\ 7 & - 21 & 56 \end{array}]$
17. $A B = [\begin{array}{r} 45 \\ 327 \end{array}],$ $A B = [\begin{array}{r} 45 \\ 327 \end{array}],$ BA not defined
19. $A I = I A = A$ $A I = I A = A$
21. $A I = I A = A$ $A I = I A = A$
23. $B = A^{- 1}$ $B = A^{- 1}$
25. $B = A^{- 1}$ $B = A^{- 1}$
27. Yes
29. No
31. $A^{2} = A$ $A^{2} = A$
33. $B^{3} = B$ $B^{3} = B$
35. $[\begin{array}{r} a c + b d & a d + b c \\ b c + a d & b d + a c \end{array}]$ $[\begin{array}{r} a c + b d & a d + b c \\ b c + a d & b d + a c \end{array}]$
37. $[\begin{array}{r} - 1 & 0 \\ 0 & - 1 \end{array}] [\begin{array}{r} - 1 & 0 \\ 0 & - 1 \end{array}] = [\begin{array}{r} 1 & 0 \\ 0 & 1 \end{array}]$ $[\begin{array}{r} - 1 & 0 \\ 0 & - 1 \end{array}] [\begin{array}{r} - 1 & 0 \\ 0 & - 1 \end{array}] = [\begin{array}{r} 1 & 0 \\ 0 & 1 \end{array}]$
39. $A^{2} - I = (A + I) (A - I) = [\begin{array}{r} 15 & 28 \\ 21 & 36 \end{array}]$ $A^{2} - I = (A + I) (A - I) = [\begin{array}{r} 15 & 28 \\ 21 & 36 \end{array}]$
41. 45.2%
43. $[\begin{array}{r} 0 & - j \\ j & 0 \end{array}] [\begin{array}{r} 0 & - j \\ j & 0 \end{array}] = [\begin{array}{r} 1 & 0 \\ 0 & 1 \end{array}]$ $[\begin{array}{r} 0 & - j \\ j & 0 \end{array}] [\begin{array}{r} 0 & - j \\ j & 0 \end{array}] = [\begin{array}{r} 1 & 0 \\ 0 & 1 \end{array}]$
45. $v_{2} = v_{1}, i_{2} = - v_{1} / R + i_{1}$ $v_{2} = v_{1}, i_{2} = - v_{1} / R + i_{1}$
47. Ellipse

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Table of Contents for Exercises 16.2, page 447

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Table of Contents for
Exercises 16.2, page 447