Solutions

Solutions to Try Its

1. A+B=[2116   0−3]+[31−4−253]=[2+31+11+(−4)6+(−2)0+5−3+3]=[52−3450]

2. −2B=[−8−2−6−4]

Solutions to Odd-Numbered Exercises

1. No, they must have the same dimensions. An example would include two matrices of different dimensions. One cannot add the following two matrices because the first is a 2×2 matrix and the second is a 2×3 matrix. [1234]+[654321] has no sum.

3. Yes, if the dimensions of A are m×n and the dimensions of B are n×m, both products will be defined.

5. Not necessarily. To find AB, we multiply the first row of A by the first column of B to get the first entry of AB. To find BA, we multiply the first row of B by the first column of A to get the first entry of BA. Thus, if those are unequal, then the matrix multiplication does not commute.

7. [111915941767]

9. [−4281]

11. Undidentified; dimensions do not match

13. [92763360192]

15. [−64−12−28−72−360−20−12−116]

17. [1,8001,2001,3008001,4006007004002,100]

19. [201022828]

21. [60412−16120−216]

23. [−6824136−54−1264−5730128]

25. Undefined; dimensions do not match.

27. [−841−340−15−1442742]

29. [−840650−530330360250−10900110]

31. [−3501,050350350]

33. Undefined; inner dimensions do not match.

35. [1,400700−1,400700]

37. [332,500927,500−227,50087,500]

39. [490,00000490,000]

41. [−234−79−7]

43. [−42921−27−31]

45. [−3−2−2−285946−4167]

47. [1−18−9−198505369−7212691]

49. [01.69−1]

51. [224−4.51232−9−86461]

53. [0.530.521210710]

55. [100010001]

57. [100010001]

59. Bn=

Bn= even[100010001]

Bn= odd[100001010]