CHAPTER 01 6e
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 1)
2x1 + x3 = 0
x1 + 5x2 + x3 = 40
A) (-8, 0, 0) B) (0, -8, -8) C) (8, 8, 0) D) (0, 8, 0)
2) x1 + 3x2 + 2x3 = 11 2)
4x2 + 9x3 = -12
x3 = -4
A) (-4, 1, 6) B) (1, 6, -4) C) (1, -4, 6) D) (-4, 6, 1)
3) x1 - x2 + 8x3 = -107 3)
6x1 + 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 4)
2x1 + 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 5)
x1 - x3 = -2
x2 + 3x3 = 11
A) No solution B) (0, 1, 2) C) (-1, 2, -3) D) (1, 2, 3)
6) x1 + x2 + x3 = 7 6)
x1 - x2 + 2x3 = 7
5x1 + x2 + x3 = 11
A) (4, 2, 1) B) (1, 2, 4) C) (1, 4, 2) D) (4, 1, 2)
7) x1 - x2 + x3 = 8 7)
x1 + x2 + x3 = 6
x1 + x2 - x3 = -12
A) (2, -1, -9) B) (-2, -1, -9) C) (-2, -1, 9) D) (2, -1, 9)
1
, 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) (1, -1, 1) B) (0, 1, 0) C) (0, 0, 1) D) (-1, 1, 1)
10) 2x1 + x2 =0 10)
x1 - 3x2 + x3 = 0
3x1 + x2 - x3 = 0
A) (0, 1, 0) B) (1, 0, 0) C) (0, 0, 0) D) No solution
Determine whether the system is consistent.
11) x1 + x2 + x3 = 7 11)
x1 - x2 + 2x3 = 7
5x1 + x2 + x3 = 11
A) Yes B) No
12) 5x1 + 2x2 + x3 = -11 12)
2x1 - 3x2 - x3 = 17
7x1 + x2 + 2x3 = -4
A) No B) Yes
13) 4x1 - x2 + 3x3 = 12 13)
2x1 + 9x3 = -5
x1 + 4x2 + 6x3 = -32
A) Yes B) No
14) 2x1 + x2 =0 14)
x1 - 3x2 + x3 = 0
3x1 + x2 - x3 = 0
A) No B) Yes
15) x1 + x2 + x3 = 6 15)
x1 - x3 = -2
x2 + 3x3 = 11
A) No B) Yes
2
, 16) 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) Yes B) No
19) 5x1 + 2x2 + x3 = -11 19)
2x1 - 3x2 - x3 = 17
7x1 - x2 = 12
A) Yes B) No
20) 5x2 + x4 = -21 20)
x1 + x2 + 4x3 - x4 = 4
5x1 + x3 + 4x4 = 12
x1 + x2 + 6x3 =5
A) Yes B) No
Determine whether the matrix is in echelon form, reduced echelon form, or neither.
1 3 5 -7
21) 0 1 -4 -4 21)
0 0 1 6
A) Reduced echelon form B) Echelon form C) Neither
1 4 5 -7
22) 0 1 -4 -5 22)
0 6 1 4
A) Neither B) Echelon form C) Reduced echelon form
1 4 5 -7
23) 3 1 -4 -6 23)
0 4 1 3
A) Neither B) Echelon form C) Reduced echelon form
3
, 1 0 0 -7
24) 1 1 0 1 24)
0 3 1 1
A) Echelon form B) Neither C) Reduced echelon form
1 4 1 -7
25) 0 1 -4 7 25)
0 0 0 0
A) Reduced echelon form B) Neither C) Echelon form
1 0 5 -4
26) 0 1 -5 -2 26)
0 0 0 0
0 0 0 0
A) Reduced echelon form B) Neither C) Echelon form
1 -5 -5 -5
27) 0 0 -2 3 27)
0 0 0 -3
0 0 0 0
A) Neither B) Echelon form C) Reduced echelon form
Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.
28) Find the echelon form of the given matrix. 28)
1 4 -2 3
-3 -11 9 -5
-2 4 -3 4
A) B)
1 4 -2 3 1 4 -2 3
0 1 3 4 0 1 3 4
0 12 -7 10 0 0 -19 -2
C) D)
1 4 -2 3 1 4 -2 3
0 1 3 4 0 1 3 4
0 0 -43 0 0 0 -43 -38
4
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 1)
2x1 + x3 = 0
x1 + 5x2 + x3 = 40
A) (-8, 0, 0) B) (0, -8, -8) C) (8, 8, 0) D) (0, 8, 0)
2) x1 + 3x2 + 2x3 = 11 2)
4x2 + 9x3 = -12
x3 = -4
A) (-4, 1, 6) B) (1, 6, -4) C) (1, -4, 6) D) (-4, 6, 1)
3) x1 - x2 + 8x3 = -107 3)
6x1 + 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 4)
2x1 + 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 5)
x1 - x3 = -2
x2 + 3x3 = 11
A) No solution B) (0, 1, 2) C) (-1, 2, -3) D) (1, 2, 3)
6) x1 + x2 + x3 = 7 6)
x1 - x2 + 2x3 = 7
5x1 + x2 + x3 = 11
A) (4, 2, 1) B) (1, 2, 4) C) (1, 4, 2) D) (4, 1, 2)
7) x1 - x2 + x3 = 8 7)
x1 + x2 + x3 = 6
x1 + x2 - x3 = -12
A) (2, -1, -9) B) (-2, -1, -9) C) (-2, -1, 9) D) (2, -1, 9)
1
, 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) (1, -1, 1) B) (0, 1, 0) C) (0, 0, 1) D) (-1, 1, 1)
10) 2x1 + x2 =0 10)
x1 - 3x2 + x3 = 0
3x1 + x2 - x3 = 0
A) (0, 1, 0) B) (1, 0, 0) C) (0, 0, 0) D) No solution
Determine whether the system is consistent.
11) x1 + x2 + x3 = 7 11)
x1 - x2 + 2x3 = 7
5x1 + x2 + x3 = 11
A) Yes B) No
12) 5x1 + 2x2 + x3 = -11 12)
2x1 - 3x2 - x3 = 17
7x1 + x2 + 2x3 = -4
A) No B) Yes
13) 4x1 - x2 + 3x3 = 12 13)
2x1 + 9x3 = -5
x1 + 4x2 + 6x3 = -32
A) Yes B) No
14) 2x1 + x2 =0 14)
x1 - 3x2 + x3 = 0
3x1 + x2 - x3 = 0
A) No B) Yes
15) x1 + x2 + x3 = 6 15)
x1 - x3 = -2
x2 + 3x3 = 11
A) No B) Yes
2
, 16) 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) Yes B) No
19) 5x1 + 2x2 + x3 = -11 19)
2x1 - 3x2 - x3 = 17
7x1 - x2 = 12
A) Yes B) No
20) 5x2 + x4 = -21 20)
x1 + x2 + 4x3 - x4 = 4
5x1 + x3 + 4x4 = 12
x1 + x2 + 6x3 =5
A) Yes B) No
Determine whether the matrix is in echelon form, reduced echelon form, or neither.
1 3 5 -7
21) 0 1 -4 -4 21)
0 0 1 6
A) Reduced echelon form B) Echelon form C) Neither
1 4 5 -7
22) 0 1 -4 -5 22)
0 6 1 4
A) Neither B) Echelon form C) Reduced echelon form
1 4 5 -7
23) 3 1 -4 -6 23)
0 4 1 3
A) Neither B) Echelon form C) Reduced echelon form
3
, 1 0 0 -7
24) 1 1 0 1 24)
0 3 1 1
A) Echelon form B) Neither C) Reduced echelon form
1 4 1 -7
25) 0 1 -4 7 25)
0 0 0 0
A) Reduced echelon form B) Neither C) Echelon form
1 0 5 -4
26) 0 1 -5 -2 26)
0 0 0 0
0 0 0 0
A) Reduced echelon form B) Neither C) Echelon form
1 -5 -5 -5
27) 0 0 -2 3 27)
0 0 0 -3
0 0 0 0
A) Neither B) Echelon form C) Reduced echelon form
Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.
28) Find the echelon form of the given matrix. 28)
1 4 -2 3
-3 -11 9 -5
-2 4 -3 4
A) B)
1 4 -2 3 1 4 -2 3
0 1 3 4 0 1 3 4
0 12 -7 10 0 0 -19 -2
C) D)
1 4 -2 3 1 4 -2 3
0 1 3 4 0 1 3 4
0 0 -43 0 0 0 -43 -38
4
