College Algebra 9th txtbk

454 CHAPTER 7 SYSTEMS OF EQUATIONS AND MATRICES
5. x 1 1, x 2 1, x 3 0 or (1, 1, 0)
6. No solution
7. x 1 5t 4, x 2 3t 5, x 3 t, t any real number; or {(5t 4, 3t 5, t) | t any real number}
8. x 1 s 7, x 2 s, x 3 t 2, x 4 3t 1, x 5 t, s and t any real numbers; or
{(s 7, s, t 2, 3t 1, t) | s and t any real numbers}
9.
18-Passenger 24-Passenger 42-Passenger
Planes Planes Planes
t x 1 x 2 x 3
14 2 14 14
15 5 10 15
16 8 6 16
17 11 2 17
7-2 Exercises
1. What is the size of a matrix?
2. What is a row matrix? What is its size?
3. What is a column matrix? What is its size?
4. What is a square matrix?
a ij
5. What does mean?
6. What is the principal diagonal of a matrix?
7. What is an augmented coefficient matrix?
8. What operations can you perform on an augmented coefficient
matrix to produce a row-equivalent matrix?
9. What is a reduced matrix and how is it used to solve a system of
linear equations?
10. Describe the Gauss–Jordan elimination process in your own
words.
` ` £
` `
In Problems 11–18, indicate whether each matrix is in reduced form.
11. 12. c 1 0 5
0 2 6 d
0 1 3 d
0 1 2 0
1 1 4 0
13. £ 0 0 0 † 1 §
14. £ 0 0 0 † 0 §
0 0 0 0
0 0 0 1
0 0 1 2
1 2 4 1
15. £ 0 1 0 † 5 §
16. 0 0 1 † 3 §
17. 18. c 0 0 1 0 0 0 1 1 d 0 0 0 0 d
1 0 0 4
0 0 0 0
In Problems 19–26, write the linear system corresponding to each
reduced augmented matrix and solve.
1 0 0 0 2
1 0 0 2
0 1 0 0 0
19. £ 0 1 0 † 3 §
20. ≥
∞ ¥
0 0 1 0 1
0 0 1 0
0 0 0 1 3
1 0 2 3
21. £ 0 1 1 † 5 § 22.
0 0 0 0
£
`
1 0 0
23. £ 0 1 † 0 §
24.
1 2 0 3
25. c 26.
0 0 1 3 2 d
0 0 1
1 2 0
£ 0 0 1 †
0 0 0
1 0
0 1 †
0 0
5
§
3
0
3
5 §
0
`
`
1
2)R 2
c 1 0 2 3 4
0 1 1 2 1 d
Perform each of the row operations indicated in Problems 27–38
on the following matrix:
c 1 3 2
4 6 8 d
27. R 1 4 R 2
1
28. 2R 2 S R 2 29. 4R 1 S R 1
30. 2R 1 S R 1 31. 2R 2 S R 2 32. 1R 2 S R 2
33. (4)R 1 R 2 S R 2 34. ( R 1 S R 1
35. (2)R 1 R 2 S R 2 36. (3)R 1 R 2 S R 2
37. (1)R 1 R 2 S R 2 38. 1R 1 R 2 S R 2