[]question 1 of 20 0.0/ 5.0 points use cramer’s rule to solve the

Question 1 of 20
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

A. {( 1, -9, -6)}

 

B. {( 2, 7, 6)}

 

C. {( 9, 6, 9)}

 

D. {( 1, 9, 6)}

 
Question 2 of 20
5.0/ 5.0 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A. 

A = , B = 

A. B = A-1

 

B. B ≠ A-1

 
Question 3 of 20
5.0/ 5.0 Points
Evaluate the determinant.

A. 60

 

B. -30

 

C. -60

 

D. 30

 
Question 4 of 20
5.0/ 5.0 Points
Evaluate the determinant.

Question 5 of 20
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

A. {( 7, 1, 7)}

 

B. {( 14, 7, -7)}

 

C. {( -7, 7, 14)}

 

D. {( 7, 7, 1)}

 
Question 6 of 20
0.0/ 5.0 Points
Question 7 of 20
0.0/ 5.0 Points
Question 8 of 20
0.0/ 5.0 Points
Determinants are used to show that three points lie on the same line (are collinear). If 
= 0, 
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?
Question 9 of 20
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

Question 10 of 20
0.0/ 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 11 of 20
0.0/ 5.0 Points
Find the inverse of the matrix, if possible. 

A = 

Question 12 of 20
0.0/ 5.0 Points
Find the product AB, if possible. 

A = , B = 

Question 13 of 20
0.0/ 5.0 Points
Question 14 of 20
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

A. system is inconsistent

 

B. system contains dependent equations

 
Question 15 of 20
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,  )}
 

B. {(1, -2, 0, 3)}

 
C. {( , -2, 0, )}
 
 
Question 16 of 20
0.0/ 5.0 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A. 
A = , B = 

A. B = A-1

 

B. B ≠ A-1

 
Question 17 of 20
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

Question 18 of 20
0.0/ 5.0 Points
Give the order of the matrix, and identify the given element of the matrix.

; a12

A. 4 × 2; -11

 

B. 4 × 2; 14

 

C. 2 × 4; 14

 

D. 2 × 4; -11

 
Question 19 of 20
0.0/ 5.0 Points
Let A = and B = . Find A – 3B.
Question 20 of 20
0.0/ 5.0 Points
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