Linear Algebra and Its Applications, 6th edition By David C. Lay
Email: richard@qwconsultancy.com
Exam Name___________________________________
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
1)
+ x3 = 0
x1 + 5x2 + x3 = 40
A) (8, 8, 0)
B) (0, -8, -8)
C) (-8, 0, 0)
D) (0, 8, 0)
2) x1 + 3x2 + 2x3 = 11
2)
4x2 + 9x3 = -12 x3 = -4
A) (1, -4, 6)
B) (-4, 1, 6)
C) (-4, 6, 1)
D) (1, 6, -4)
3) x1 - x2 + 8x3 = -107 6x1
3)
+ x3 = 17 3x2 - 5x3 = 89
A) (5, -8, -13)
B) (5, 8, -13)
C) (-5, -8, 13)
D) (-5, 8, 13)
4) 4x1 - x2 + 3x3 = 12 2x1
4)
+ 9x3 = -5
x1 + 4x2 + 6x3 = -32
A) (2, 7, -1)
B) (2, 7, 1)
C) (2, -7, 1)
D) (2, -7, -1)
5) x1 + x2 + x3 = 6 x1
5)
- x3 = -2 x2 + 3x3 = 11
A) (0, 1, 2)
B) No solution
C) (1, 2, 3)
D) (-1, 2, -3)
6) x1 + x2 + x3 = 7
6)
x1 - x2 + 2x3 = 7 5x1 + x2 + x3 = 11
A) (4, 1, 2)
B) (4, 2, 1)
C) (1, 4, 2)
1
D) (1, 2, 4)
7) x1 - x2 + x3 = 8
7)
x1 + x 2 + x 3 = 6 x1 + x2 - x3 = -12
A) (2, -1, -9)
B) (2, -1, 9)
C) (-2, -1, 9)
D) (-2, -1, -9)
8) 5x1 + 2x2 + x3 = -11
8)
2x1 - 3x2 - x3 = 17 7x1 + x2 + 2x3 = -4
A) (3, 0, -4)
B) (0, 6, -1)
C) (-3, 0, 4)
D) (0, -6, 1)
9) 7x1 + 7x2 + x3 = 1
9)
x1 + 8x2 + 8x3 = 8 9x1 + x2 + 9x3 = 9
A) (0, 1, 0) 10) 2x1 + x2
B) (0, 0, 1)
C) (1, -1, 1)
D) (-1, 1, 1)
=0
10)
x1 - 3x2 + x3 = 0 3x1 + x2 - x3 = 0
A) (0, 1, 0)
B) (0, 0, 0)
C) No solution
Determine whether the system is consistent. 11) x1 + x2 + x3 = 7
D) (1, 0, 0)
11)
x1 - x2 + 2x3 = 7 5x1 + x2 + x3 = 11
A) No
B) Yes
12) 5x1 + 2x2 + x3 = -11
12)
2x1 - 3x2 - x3 = 17 7x1 + x2 + 2x3 = -4
A) No
B) Yes
13) 4x1 - x2 + 3x3 = 12 2x1
13)
+ 9x3 = -5
x1 + 4x2 + 6x3 = -32
A) Yes 14) 2x1 + x2
B) No =0
14)
x1 - 3x2 + x3 = 0 3x1 + x2 - x3 = 0
A) Yes
B) No
2
15) x1 + x2 + x3 = 6 x1
15)
- x3 = -2 x2 + 3x3 = 11
A) No 16)
B) Yes
x1 - x2 + 3x3 = -11
16)
-4x1 + 4x2 - 12x3 = -2 x1 + 3x2
+ x3 = -17
A) Yes
B) No
17) x1 + x2 + x3 = 7
17)
x1 - x2 + 2x3 = 7 2x1
+ 3x3 = 15
A) No
B) Yes
18) x1 + 3x2 + 2x3 = 11
18)
4x2 + 9x3 = -12 x1 + 7x2 + 11x3 = -11
A) No
B) Yes
19) 5x1 + 2x2 + x3 = -11
19)
2x1 - 3x2 - x3 = 17 7x1 - x2
= 12
A) Yes
B) No
5x2
20)
+ x4 = -21
20)
x1 + x2 + 4x3 - x4 = 4 5x1
+ x3 + 4x4 = 12
x1 + x2 + 6x3
=5
A) No
B) Yes
Determine whether the matrix is in echelon form, reduced echelon form, or neither. 1 3 5 -7 21) 0 1 -4 -4 0 0 1 6
A) Reduced echelon form
B) Echelon form
3
C) Neither
21)
1 4
5 -7
0 6
1
22) 0 1 -4 -5
22)
4
A) Reduced echelon form 1 4
5 -7
0 4
1
B) Echelon form
C) Neither
23) 3 1 -4 -6
23)
3
A) Reduced echelon form
B) Echelon form
C) Neither
1 0 0 -7 1 0 3 1 1
24) 1 1 0
A) Reduced echelon form 1 4
24) B) Neither
C) Echelon form
1 -7 7 0 0
25) 0 1 -4 0 0
A) Reduced echelon form
26)
1 0 0 0
B) Neither
C) Echelon form
0 5 -4 1 -5 -2 0 0 0 0 0 0
A) Neither
27)
25)
26)
B) Reduced echelon form
C) Echelon form
1 -5 -5 -5 0 0 -2 3 0 0 0 -3 0 0 0 0
A) Neither
27)
B) Echelon form
4
C) Reduced echelon form