# []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)}
0.0/ 5.0 Points
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 =

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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