Question 1 of 20
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0.0/ 5.0 Points |
Use Cramer’s rule to solve the system. 2x + 4y – z = 32 x – 2y + 2z = -5 5x + y + z = 20
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A. {( 1, -9, -6)}
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B. {( 2, 7, 6)}
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C. {( 9, 6, 9)}
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D. {( 1, 9, 6)}
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Question 2 of 20
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5.0/ 5.0 Points |
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A =  , B = 
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Question 3 of 20
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5.0/ 5.0 Points |
Evaluate the determinant.
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A. 60
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B. -30
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C. -60
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D. 30
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Question 4 of 20
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5.0/ 5.0 Points |
Evaluate the determinant.
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Question 5 of 20
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0.0/ 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
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A. {( 7, 1, 7)}
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B. {( 14, 7, -7)}
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C. {( -7, 7, 14)}
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D. {( 7, 7, 1)}
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Question 6 of 20
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0.0/ 5.0 Points |
Solve the matrix equation for X.
Let A =  and B =  ; 4X + A = B
A. X =  |
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B. X =  |
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C. X =  |
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D. X =  |
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Question 7 of 20
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Find the product AB, if possible.
A =  , B = 
A.  |
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B.  |
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C.  |
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D. AB is not defined.
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Question 8 of 20
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Determinants are used to show that three points lie on the same line (are collinear). If  = 0, then the points ( x 1, y 1), ( x 2, y 2), and ( x 3, y 3) 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?
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Question 9 of 20
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0.0/ 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
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Question 10 of 20
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0.0/ 5.0 Points |
Let B = [-1 3 6 -3]. Find -4B.
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A. [-4 12 24 -12]
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B. [-3 1 4 -5]
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C. [4 -12 -24 12]
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D. [4 3 6 -3]
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Question 11 of 20
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0.0/ 5.0 Points |
Find the inverse of the matrix, if possible.
A = 
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Question 12 of 20
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0.0/ 5.0 Points |
Find the product AB, if possible.
A =  , B = 
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Question 13 of 20
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0.0/ 5.0 Points |
Find the product AB, if possible.
A =  , B = 
A.  |
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B.  |
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C.  |
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D. AB is not defined.
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Question 14 of 20
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0.0/ 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
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A. system is inconsistent
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B. system contains dependent equations
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Question 15 of 20
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0.0/ 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, –  , 0,  )} |
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B. {(1, -2, 0, 3)}
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C. {(  , -2, 0,  )} |
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Question 16 of 20
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0.0/ 5.0 Points |
Find the products AB and BA to determine whether B is the multiplicative inverse of A. A =  , B = 
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Question 17 of 20
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0.0/ 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, –  ,  )} |
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B. {(1, –  ,  , 6)} |
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C. ∅
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Question 18 of 20
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0.0/ 5.0 Points |
Give the order of the matrix, and identify the given element of the matrix.
 ; a12
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A. 4 × 2; -11
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B. 4 × 2; 14
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C. 2 × 4; 14
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D. 2 × 4; -11
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Question 19 of 20
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0.0/ 5.0 Points |
Let A =  and B =  . Find A – 3B.
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Question 20 of 20
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0.0/ 5.0 Points |
Find the product AB, if possible. A =  , B = 
A.  |
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B. AB is not defined.
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C.  |
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D.  |
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