AEM_3e_Chapter08

AEM_3e_Chapter08 - 8 1. 2 4 6. 8 1 Matrices EXERCISES 8.1...

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8 8 Matrices EXERCISES 8.1 Matrix Algebra 1. 2 × 4 2. 3 × 2 3. 3 × 3 4. 1 × 3 5. 3 × 4 6. 8 × 1 7. Not equal 8. Not equal 9. Not equal 10. Not equal 11. Solving x = y 2, y =3 x 2 we obtain x =2, y =4. 12. Solving x 2 =9, y =4 x we obtain x =3, y = 12 and x = 3, t = 12. 13. c 23 = 2(0) 3( 3) = 9; c 12 = 2(3) 3( 2) = 12 14. c 23 = 2(1) 3(0) = 2; c 12 =2( 1) 3(0) = 2 15. (a) A + B = µ 4 2 5+6 6+8 9 10 = µ 21 1 2 1 (b) B A = µ 2 46 5 8+6 10 9 = µ 61 14 19 (c) 2 A +3 B = µ 81 0 12 18 + µ 8 24 30 = µ 22 8 12 12 16. (a) A B = 2 3 0+1 4 01 2 7+4 3+2 = 51 4 1 11 5 (b) B A = 3+2 1 0 0 42 1 4 7 2 3 = 5 1 41 11 5 (c) 2( A + B )=2 1 1 43 31 = 2 2 86 62 17. (a) AB = µ 2 91 2 6 5+12 30+8 = µ 11 6 17 22 (b) BA = µ 2 30 3+24 6 10 9+8 = µ 32 27 4 1 (c) A 2 = µ 4+15 6 12 10 20 15 + 16 = µ 19 18 30 31 373
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8.1 Matrix Algebra (d) B 2 = µ 1+18 6+12 3+6 18+4 = µ 19 6 32 2 18. (a) AB = 4+4 6 12 3+8 20+10 30 30 15+20 32+12 48 36 24+24 = 0 65 10 0 5 20 12 0 (b) BA = µ 4+30 24 16+60 36 1 15+16 4 30+24 = µ 28 2 2 19. (a) BC = µ 92 4 38 (b) A ( BC )= µ 1 2 24 ¶µ 4 = µ 6 16 (c) C ( BA µ 02 34 00 = µ (d) A ( B + C µ 1 2 55 = µ 4 5 81 0 20. (a) AB =(5 67 ) 3 4 1 =( 16) (b) BA = 3 4 1 (5 15 18 21 20 24 28 56 7 (c) ( BA ) C = 15 18 21 20 24 28 7 12 4 01 1 32 1 = 78 54 99 104 72 132 26 18 33 (d) Since AB is 1 × 1 and C is 3 × 3 the product ( AB ) C is not defned. 21. (a) A T A =(4 8 10) 4 8 10 = (180) (b) B T B = 2 4 5 ( 245 481 0 62 0 10 20 25 (c) A + B T = 4 8 10 + 2 4 5 = 6 12 5 22. (a) A + B T = µ 12 + µ 25 37 = µ 17 51 1 (b) 2 A T B T = µ 48 µ = µ 4 1 11 374
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8.1 Matrix Algebra (c) A T ( A B )= µ 12 24 ¶µ 3 1 3 3 = µ 3 7 6 14 23. (a) ( AB ) T = µ 71 0 38 75 T = µ 73 8 10 75 (b) B T A T = µ 5 2 10 5 38 41 = µ 8 10 75 24. (a) A T + B = µ 5 4 96 + µ 31 1 72 = µ 27 28 (b) 2 A + B T = µ 10 18 81 2 + µ 3 7 11 2 = µ 1 4 25. µ 4 8 µ 4 16 + µ 6 9 = µ 14 1 26. 6 3 3 + 5 5 15 + 6 8 10 = 5 10 22 27.
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AEM_3e_Chapter08 - 8 1. 2 4 6. 8 1 Matrices EXERCISES 8.1...

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