1. [43−32∣114]
2. x−y+z=52x−y+3z=1y+z=−9
3. (2,1)
4. 100−25102551∣21792
5. (1,1,1)
6. $150,000 at 7%, $750,000 at 8%, $600,000 at 10%
Solutions to Odd-Numbered Exercises
1. Yes. For each row, the coefficients of the variables are written across the corresponding row, and a vertical bar is placed; then the constants are placed to the right of the vertical bar.
3. No, there are numerous correct methods of using row operations on a matrix. Two possible ways are the following: (1) Interchange rows 1 and 2. Then R2=R2−9R1. (2) R2=R1−9R2. Then divide row 1 by 9.
5. No. A matrix with 0 entries for an entire row would have either zero or infinitely many solutions.
7. [0916−1∣42]
9. 1123534809∣164−7
11. −2x+5y=56x−18y=26
13. 3x+2y=13−x−9y+4z=538x+5y+7z=80
15. 4x+5y−2z=12y+58z=28x+7y−3z=−5
17. No solutions
19. (−1,−2)
21. (6,7)
23. (3,2)
25. (51,21)
27. (x,154(5x+1))
29. (3,4)
31. (39196,−135)
33. (31,−42,87)
35. (4021,201,89)
37. (1318,1315,−1315)
39. (x,y,21(1−2x−3y))
41. (x,−2x,−1)
43. (125,−25,0)
45. (8,1,−2)
47. (1,2,3)
49. (x,2831−43x,281(−7x−3))
51. No solutions exist.
53. 860 red velvet, 1,340 chocolate
55. 4% for account 1, 6% for account 2
57. $126
59. Banana was 3%, pumpkin was 7%, and rocky road was 2%
61. 100 almonds, 200 cashews, 600 pistachios