College Algebra 9th txtbk

SECTION 7–2 Solving Systems of Linear Equations Using Gauss–Jordan Elimination 455
Use row operations to change each matrix in Problems 39–44 to 63. 2x 1 5x 2 3x 3 7
reduced form.
4x 1 10x 2 2x 3 6
39. c 1 2
40. c 1 3
0 2 ` 1
0 1 ` 1 6x 1 15x 2 x 3 19
3 d 4 d
64. 5x 1 3x 2 2x 3 13
1 0 3 1
41. £ 0 1 2 † 0 § 42.
0 0 3 6
1 2 2 1
43. £ 0 3 6 † 1 § 44.
0 1 2
Solve Problems 45–70 using Gauss–Jordan elimination.
45. x 1 4x 2 2 46. x 1 3x 2 5
2x 1 x 2 3 3x 1 x 2 5
47. x 1 2x 2 4 48. 2x 1 3x 2 2
2x 1 4x 2 8
4x 1 6x 2 7
49. 3x 1 6x 2 9 50. 2x 1 4x 2 2
2x 1 4x 2 6 3x 1 6x 2 3
51. 2x 1 4x 2 10x 3 2
3x 1 9x 2 21x 3 0
x 1 5x 2 12x 3 1
52. 3x 1 5x 2 x 3 7
x 1 x 2 x 3 1
2x 1 11x 3 7
53. 3x 1 8x 2 x 3 18
2x 1 x 2 5x 3 8
2x 1 4x 2 2x 3 4
54. 2x 1 7x 2 15x 3 12
4x 1 7x 2 13x 3 10
3x 1 6x 2 12x 3 9
55. 2x 1 x 2 3x 3 8
x 1 2x 2 7
56. 2x 1 4x 2 6x 3 10
3x 1 3x 2 3x 3 6
57. 2x 1 x 2 0 58. 2x 1 x 2 0
3x 1 2x 2 7
3x 1 2x 2 7
x 1 x 2 1
x 1 x 2 2
59. 3x 1 4x 2 x 3 1
2x 1 3x 2 x 3 1
x 1 2x 2 3x 3 2
60. 2x 1 x 2 3x 3 7
x 1 4x 2 2x 3 0
x 1 3x 2 x 3 1
61.
1 3
2x 1 2x 2 4x 3 2
3x 1 3x 2 6x 3 3
62. 4x 1 x 2 2x 3 3
4x 1 x 2 3x 3 10
8x 1 2x 2 9x 3 1
1 0 4
£ 0 1 3 †
0 0 2
0 2 8
£ 2 2 6 †
0 1 4
0
1 §
2
1
4 §
1
2
66. 2x 1 4x 2 5x 3 4x 4 8
x 1 2x 2 2x 3 x 4 3
67.
68. x 1 x 2 4x 3 x 4 1.3
x 1 x 2 x 3 1.1
2x 1 x 3 3x 4 4.4
2x 1 5x 2 11x 3 3x 4 5.6
69.
70.
2x 1 x 2 3x 3 1
4x 1 2x 2 4x 3 12
65. x 1 2x 2 4x 3 x 4 7
2x 1 5x 2 9x 3 4x 4 16
x 1 5x 2 7x 3 7x 4 13
x 1 x 2 3x 3 2x 4 1
2x 1 4x 2 3x 3 x 4 0.5
3x 1 x 2 10x 3 4x 4 2.9
4x 1 3x 2 8x 3 2x 4 0.6
x 1 2x 2 x 3 x 4 2x 5 2
2x 1 4x 2 2x 3 2x 4 2x 5 0
3x 1 6x 2 x 3 x 4 5x 5 4
x 1 2x 2 3x 3 x 4 x 5 3
x 1 3x 2 x 3 x 4 2x 5 2
x 1 5x 2 2x 3 2x 4 2x 5 0
2x 1 6x 2 2x 3 2x 4 4x 5 4
x 1 3x 2 x 3 x 5 3
71. Consider a consistent system of three linear equations in three
variables. Discuss the nature of the solution set for the system
if the reduced form of the augmented coefficient matrix has
(A) One leftmost 1
(B) Two leftmost 1’s
(C) Three leftmost 1’s
(D) Four leftmost 1’s
72. Consider a system of three linear equations in three variables.
Give examples of two reduced forms that are not row equivalent
if the system is
(A) Consistent and dependent
(B) Inconsistent
APPLICATIONS
73. BUYING Suppose that you have a $129 credit on your account
at Amazon.com, and you want to spend it all on sale CDs at $10
each, sale DVDs at $12 each, and sale books at $7 each. If you buy
13 items total, how many will you buy of each?
74. PETTY CRIME Shady Grady finds a parking meter with a broken
lock and scoops out the change inside. The meter accepts
nickels, dimes, and quarters, and there were 32 coins inside with
a total value of $6.80. How many of each type of coin did Grady
get?
75. CHEMISTRY A chemist has two solutions of sulfuric acid: a
20% solution and an 80% solution. How much of each should be
used to obtain 100 liters of a 62% solution?