Question 30!

2/files/folder/Homeworks?preview=39002069 40b2c...: "Towar... 4.5 EXERCISES The (2 x 2) matrices listed in Eq. (9) are used in several Exercises 21-24 refer to the matrices in Eq. (9) and the of the exercises that follow. vectors in Eq. (10). 21. Find w2, where wj - Brand w2 = Awj. Calculate Q = AB. Calculate Or and verify that W2 is equal to Or. (9) 22. Find w2, where wj = Cs and W2 = Awj. Calculate . c- [7 :]. 2 - [:8] Q = AC. Calculate Qs and verify that w2 is equal to Qs. 23. Find w3, where wi = Cr, w2 = BW1, and w3 = Exercises 1-6 refer to the matrices in Eq. (9). Aw2. Calculate Q = A(BC) and verify that w3 is 1. Find (a) A + B; (b) A + C; (c) 6B; and (d) B + 3C. equal to Or. 2. Find (a) B +C; (b) 3A; (c) A +2C; and (d) C +8z. 24. Find w3, where wj = Ar, w2 = Cwj, and w3 = Bw2. Calculate Q = B(CA) and verify that w3 is 3. Find a matrix D such that A + D = B. equal to Or. 4. Find a matrix D such that A + 2D = C. 5. Find a matrix D such that A + 2B + 2D = 3B. Exercises 25-30 refer to the matrices in Eq. (9). Find each of the following. 6. Find a matrix D such that 2A + 5B+ D = 2B +3A. 25. (A + B)C 26. (A + 2B) A The vectors listed in Eq. (10) are used in several of the 27. (A + C)B 28. (B + C)Z exercises that follow. 2 29. A(BZ) 30. Z(AB) The matrices and vectors listed in Eq. (11) are used in (10) several of the exercises that follow. -[4]. "=[ ] -[3]: 8-[1 2] .-[:] 20 In Exercises 7-12, perform the indicated computation, using the vectors in Eq. (10) and the matrices in Eq. (9). 7. a) r+s 8. a) t+s v = [ 2, 4 ]. C= b) 2r + t b) r+ 3u c) 2s + u C) 2u + 3t 20 9. a) Ar 10. a) Bt b) Br b) C(r + s) D c) C(s + 3t) c) B(r + s) 11. a) (A + 2B)r 12. a) (A + C)r b) (B + C)u b) (2B + 3C)s 20 Exercises 31-41 refer to the matrices and vectors in Exercises 13-20 refer to the vectors in Eq. (10). In each Eq. (11). Find each of the following. exercise, find scalars a, and a2 that satisfy the given 31. AB and BA 32. DC equation, or state that the equation has no solution. 33. Au and VA 34. uv and vu 13. air + a2s = t 14. air + a2s = u 35. v(Bu) 36. Bu 20 15. als + ant = u 16. als + ant = r + t 37. CA 38. CB 17. as + azu = 2r +t 18. as + azu = t 39. C(Bu) 40. (AB )u and A(Bu) 19. alt + azu = 3s + 4t 20. alt + azu = 3r + 2s 41. (BA)u and B(Au) 5, 20