Ch2exam
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Chapter 2Exam
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the system of equations.1) x1 - x2 + 3x3 = -8
2x1 + x3 = 0x1 + 5x2 + x3 = 40
A) (0, 8, 0) B) (0, -8, -8) C) (8, 8, 0) D) (-8, 0, 0)Answer: A
2) 5x1 + 2x2 + x3 = -112x1 - 3x2 - x3 = 177x1 + x2 + 2x3 = -4
A) (0, -6, 1) B) (0, 6, -1) C) (3, 0, -4) D) (-3, 0, 4)Answer: A
Determine whether the system is consistent.3) x1 + x2 + x3 = 7
x1 - x2 + 2x3 = 75x1 + x2 + x3 = 11
A) No B) YesAnswer: B
4) 4x1 - x2 + 3x3 = 122x1 + 9x3 = -5x1 + 4x2 + 6x3 = -32
A) No B) YesAnswer: B
5) 2x1 + x2 = 0x1 - 3x2 + x3 = 03x1 + x2 - x3 = 0
A) Yes B) NoAnswer: A
6) x1 - x2 + 4x3 = -15-5x1 + 5x2 - 20x3 = -4x1 + 3x2 + x3 = -1
A) No B) YesAnswer: A
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Determine whether the matrix is in echelon form, reduced echelon form, or neither.
7) 1 3 5 -7 0 1 -4 1 0 0 1 8
A) Neither B) Reduced echelon form C) Echelon formAnswer: C
8) 1 4 5 -7 0 1 -4 8 0 6 1 7
A) Reduced echelon form B) Echelon form C) NeitherAnswer: C
9) 1 4 5 -72 1 -4 5 0 2 1 2
A) Reduced echelon form B) Echelon form C) NeitherAnswer: C
10) 1 0 0 -75 1 0 -3 0 4 1 5
A) Reduced echelon form B) Echelon form C) NeitherAnswer: C
11) 1 6 7 -7 0 1 -4 -9 0 0 0 0
A) Reduced echelon form B) Neither C) Echelon formAnswer: C
12)
1 0 -4 20 1 -5 -50 0 0 00 0 0 0
A) Neither B) Reduced echelon form C) Echelon formAnswer: B
13)
1 -2 -4 40 0 4 -30 0 0 -20 0 0 0
A) Reduced echelon form B) Neither C) Echelon formAnswer: C
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Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.14) Find the echelon form of the given matrix.
1 4 -2 3-3 -11 9 -5-2 -3 3 -1
A)1 4 -2 30 1 3 40 0 -16 0
B)1 4 -2 30 1 3 40 0 -6 0
C)1 4 -2 30 1 3 40 0 -16 -15
D)1 4 -2 30 1 3 40 5 -1 5
Answer: C
15) Find the reduced echelon form of the given matrix. 1 4 -5 1 2 2 5 -4 -1 4-3 -9 9 2 2
A) 1 0 0 0 14 0 1 0 0 -4 0 0 0 1 4
B) 1 4 -5 1 2 0 1 -2 1 0 0 0 0 1 4
C) 1 4 -5 0 -2 0 1 -2 0 -4 0 0 0 1 4
D) 1 0 3 0 14 0 1 -2 0 -4 0 0 0 1 4
Answer: D
The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwisestate that there is no solution.
16) 1 -5 -4 0 0 2
A) (-4, 2) B) No solution C) x1 = -4 + 5x2x2 = 2x3 is free
D) x1 = -4 + 5x2x2 is free
Answer: B
17) 1 2 -3 -19 0 1 4 4 0 0 0 1
A) x1 = -27 + 11x3x2 = 4 - 4x3x3 is free
B) x1 = -19 - 2x2 + 3x3x2 is freex3 is free
C) x1 = -27 + 11x3x2 = 4 - 4x3x3 = 1
D) No solution
Answer: D
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18) 1 2 -3 8 0 1 4 -3 0 0 0 0
A) x1 = 14 + 11x3x2 = -3 - 4x3x3 is free
B) x1 = 14 + 11x3x2 = -3 - 4x3x3 = 0
C) x1 = 8 - 2x2 + 3x3x2 is freex3 is free
D) x1 = 8 -2x2 + 3x3x2 = -3 - 4x3x3 is free
Answer: A
19) 1 0 6 5 0 1 -2 -9 0 0 0 0
A) x1 = 5 - 6x3x2 is free
x3 =92
+12
x2
B) x1 = 5 - 6x3x2 = -9 + 2x3x3 = 0
C) x1 = 5 - 6x3x2 = -9 + 2x3x3 is free
D) No solution
Answer: C
20) 1 4 -2 -3 1 0 0 1 3 5-1 -4 -2 -9 -21
A) x1 = 11 - 4x2 - 3x3x2 = 5 - 3x3x3 is free
B) x1 = - 4x2 +2x3 + 3 x4 + 1x2 is freex3 = 5 - 3x4x4 is free
C) x1 = 11 - 4x2 - 3x4x2 is freex3 = 5 - 3x4x4 = 0
D) x1 = 11 - 4x2 - 3x4x2 is freex3 = 5 - 3x4x4 is free
Answer: D
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21)1 4 6 -1 2 80 0 0 -4 3 40 0 0 0 -2 8
A) x1 = -4x2 - 6x3 + 12x2 is freex3 is freex4 = -4x5 = -4
B) x1 = -4x2 - 6x3 + 12x2 is freex3 = -4
x4 =34 x5 - 1
x5 = -4
C) x1 = -4x2 - 6x3 + x4 - 2x5 + 8x2 is freex3 is free
x4 =34
x5 - 1
x5 = -4
D) No solution
Answer: A
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