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1. Find the inverse of the matrix, if possible.
A = [0 -6] (their in the same bracket)
-2-5
a.[0-1/2]
-1/6 5/12
b.[-1/6 0]
5/12-1/2
c.[5/12-1/2]
-1/6 0
d.[5/12 1/2]
1/6 0
THESE R ALL IN THE SAME ONE BRACKET, just didnt have long ones on my computer.
2.Question 2 of 20
5.0 Points
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
x + y + z = 9
2x – 3y + 4z = 7
x – 4y + 3z = -2
A.{(-7z/5+35/5,2z/5+11/5,z)}
B.{(7z/5+34/5,2z/5-11/5,z)}
C.{(-7z/5+34/5,2z/5-11/5,z)}
D.{(z/5+34/5,2z/5+11/5,z)}
Question 3 of 20
5.0 Points
Find the product AB, if possible.
A=[3 -2 1] , B=[30]
0 4 -1 -23
A.[9 -6]
-6 16
3 -5
B.[9 -6 3]
-6 16 -5
C.[9 0]
0 12
D. AB is not defined
Question 4 of 20
5.0 Points
Let B = [-1 3 6 -3]. Find -4B.
A. [-4 12 24 -12]
B. [-3 1 4 -5]
C. [4 -12 -24 12]
D. [4 3 6 -3]
Question 5 of 20
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A =[100] , B = [1 00]
110 -1 10
111 0 -11 (ALL IN ONE BRACKET)
A. B=A^-1
B. B ≢A^-1 (a = sign with a slash)
Question 6 of 20
5.0 Points
Determinants are used to show that three points lie on the same line (are collinear). If ..
⎜^x y1 ^1⎜
⎜^x2 y2 ^1⎜
⎜^x3 y3 ^1⎜=0 (ALL IN ONE STRAIGHT LINE PARATHECE)
then the points ( x1, y1), ( x2, y2), and ( x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (-2, -1), (0, 9), (-6, -21) and collinear?
A. Yes
B. No
Question 7 of 20
5.0 Points
Solve the matrix equation for X.
Let A = [3 -3] and B =[8 0] ; 4X + A = B (ALL UNDER ONE BRAC)
-4 0 0 -6
8 -2 3 -2
A.X=[5 3]
4 -6
-5 0
B. X= [-5/4-3/4]
-1 3/2
5/4 0
C. X=[-5 3]
-4 6
5 0
D. X=[5/4 3/4]
1 -3/2
-5/4 0
(THERE ALL UNDER THE SAME BRACKET)
Question 8 of 20
5.0 Points
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
3x + 5y – 2w = -13
2x + 7z – w = -1
4y + 3z + 3w = 1
-x + 2y + 4z = -5
A. {(-1,-2-/13,0,2/5)}
B. {(1,-2,0,3)}
C. {(3/4,-2,0,3/4)}
D. {(4/3,-13/20,0,5/2)}
Question 9 of 20
5.0 Points
Solve the system of equations using matrices. Use Gauss-Jordan elimination.
3x – 7 – 7z = 7
6x + 4y – 3z = 67
-6x – 3y + z = -62
A. {( 7, 1, 7)}
B. {( 14, 7, -7)}
C. {( -7, 7, 14)}
D. {( 7, 7, 1)}
Question 10 of 20
5.0 Points
Let A =[1] and B =[-1] . Find A – 3B.
-3 3
2 -2 (ALL UNDER THE SAME BRACKET)
A.[4]
-12
8
B.[-4]
12
-8
C.[-2]
6
-4
D.[4]
-6
4
Question 11 of 20
5.0 Points
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
3x – 2y + 2z – w = 2
4x + y + z + 6w = 8
-3x + 2y – 2z + w = 5
5x + 3z – 2w = 1
A.{(2,0,-3/37,9/37)}
B.{(1,-1/3,4/9,6)}
C. ∅
D.{(1/2,0,-37/3,37/9)}
Question 12 of 20
5.0 Points
Use Cramer’s rule to solve the system. 2x + 4y – z = 32 x – 2y + 2z = -5 5x + y + z = 20
A. {( 1, -9, -6)}
B. {( 2, 7, 6)}
C. {( 9, 6, 9)}
D. {( 1, 9, 6)}
Question 13 of 20
5.0 Points
Evaluate the determinant.
⎜1/6 1/8⎟
-6/5 10/7 (UNDER SAME BRACKET)
A. 1/105
B. 37/420
C. 53/140
D. 163/420
Question 14 of 20
5.0 Points
Give the order of the matrix, and identify the given element of the matrix.
[10 -11 8 -4]
14 13 -8 11 ; a12 (ALL UNDER SAME BRAC)
A. 4 × 2; -11
B. 4 × 2; 14
C. 2 × 4; 14
D. 2 × 4; -11
Question 15 of 20
5.0 Points
Find the product AB, if possible.
A =[2 -14] , B = [9]
-4 -9 2 1
3 (ALL UNDER SAME BRACKETS)
A.[29]
-39
B. AB NOT DEFINED
C. [2 -14]
-4 -9 2
9 1 3
D.[29-39]
Question 16 of 20
5.0 Points
Find the product AB, if possible.
A =[1 -6 1] , B = [-4 -5 1]
-8 -1 -9 -3 3 -4
-4 -1 -9 -1 4 9
NOT MULTIPLE CHOICE
Question 17 of 20
5.0 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A = [5 3], B = [2 -3]
3 2 -3 5
A. B = A-1
B. B ≠ A-1
Question 18 of 20
5.0 Points
Find the product AB, if possible.
A =[5 4 -3] , B = [4]
-5 -3 -2 2
-7
A.[49-12]
B.[49]
-12
C.[5 4 -3]
-5 -3 -2 (UNDER ONE BRACKET)
4 2 -7
D. AB is not defined
Question 19 of 20
5.0 Points
Evaluate the determinant.
⎜-35 -2⎟
30 -3
30 1 (UNDER ONE BRACKET)
A. 60
B. -30
C. -60
D. 30
Question 20 of 20
5.0 Points
Use Cramer’s rule to determine if the system is inconsistent system or contains dependent equations.
2x + 7 = 8
6x + 3y = 24
A. system is inconsistent
B. system contains dependent equations
