Chapter 8

Chapter 8 - 8 Matrices Exercises 8.1 1 2 4 6 8 1 2 3 2 7...

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8 Matrices Exercises 8.1 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 = · 4 25 + 6 6+8 9 10 ¸ = · 21 1 2 1 ¸ (b) B A = · 2 46 5 8+6 10 9 ¸ = · 61 14 19 ¸ (c) 2 A +3 B = · 81 0 12 18 ¸ + · 8 24 30 ¸ = · 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 = · 2 91 2 6 5+12 30 + 8 ¸ = · 11 6 17 22 ¸ (b) BA = · 2 30 3 + 24 6 10 9+8 ¸ = · 32 27 4 1 ¸ (c) A 2 = · 4+15 6 12 10 20 15 + 16 ¸ = · 19 18 30 31 ¸ (d) B 2 = · 1+18 6+12 3+6 18+4 ¸ = · 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 0 313
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Exercises 8.1 (b) BA = · 4+30 24 16+60 36 1 15 + 16 4 30+24 ¸ = · 28 2 2 ¸ 19. (a) BC = · 92 4 38 ¸ (b) A ( BC )= · 1 2 24 ¸· 4 ¸ = · 6 16 ¸ (c) C ( BA · 02 34 00 ¸ = · ¸ (d) A ( B + C · 1 2 65 55 ¸ = · 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 48 1 0 62 0 10 20 25 (c) A + B T = 4 8 10 + 2 4 5 = 6 12 5 22. (a) A + B T = · 12 ¸ + · 25 37 ¸ = · 17 5 11 ¸ (b) 2 A T B T = · ¸ · ¸ = · 4 1 11 ¸ (c) A T ( A B · 3 1 3 3 ¸ = · 3 7 6 14 ¸ 23. (a) ( AB ) T = · 71 0 38 75 ¸ T = · 73 8 10 75 ¸ 314
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Exercises 8.1 (b) B T A T = · 5 2 10 5 ¸· 38 41 ¸ = · 73 8 10 75 ¸ 24. (a) A T + B = · 5 4 96 ¸ + · 31 1 72 ¸ = · 27 28 ¸ (b) 2 A + B T = · 10 18 81 2 ¸ + · 3 7 11 2 ¸ = · 71 1 4 ¸ 25. · 4 8 ¸ · 4 16 ¸ + · 6 9 ¸ = · 14 1 ¸ 26. 6 3 3 + 5 5 15 + 6 8 10 = 5 10 22 27.
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Chapter 8 - 8 Matrices Exercises 8.1 1 2 4 6 8 1 2 3 2 7...

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