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Question 1 of 40        

If AB = -BA, then A and B are said to be anticommutative.

Are A =                       0

1            -1

0                      and B =                       1

0          0

  -1                   anticommutative?

A.AB = -AB so they are not anticommutative.       

B. AB = BA so they are anticommutative.   

C. BA = -BA so they are not anticommutative.        

D. AB = -BA so they are anticommutative.  

Question 2 of 40        

Use Gaussian elimination to find the complete solution to each system.

            x₁ + 4x₂ + 3x₃ - 6x₄ = 5

x₁ + 3x₂ + x₃ - 4x₄ = 3

2x₁ + 8x₂ + 7x₃ - 5x₄ = 11

2x₁ + 5x₂ - 6x₄ = 4

A. {(-47t + 4, 12t, 7t + 1, t)} 

B. {(-37t + 2, 16t, -7t + 1, t)}

C. {(-35t + 3, 16t, -6t + 1, t)}

D. {(-27t + 2, 17t, -7t + 1, t)}

Question 3 of 40        

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.



            3x₁ + 5x₂ - 8x₃ + 5x₄ = -8

 x₁ + 2x₂ - 3x₃ + x₄ = -7

2x₁ + 3x₂ - 7x₃ + 3x₄ = -11

4x₁ + 8x₂ - 10x₃+ 7x₄ = -10

A. {(1, -5, 3, 4)}        

B. {(2, -1, 3, 5)}        

C. {(1, 2, 3, 3)}          

D. {(2, -2, 3, 4)}        

Question 4 of 40        

Use Cramer’s Rule to solve the following system.



            4x - 5y = 17

2x + 3y = 3

A. {(3, -1)}    

B. {(2, -1)}    

C. {(3, -7)}    

D. {(2, 0)}     

Question 5 of 40        

Use Gauss-Jordan elimination to solve the system.

            -x - y - z = 1

4x + 5y = 0

y - 3z = 0

A. {(14, -10, -3)}       

B. {(10, -2, -6)}         

C. {(15, -12, -4)}       

D. {(11, -13, -4)}       

Question 6 of 40        

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

            8x + 5y + 11z = 30

-x - 4y + 2z = 3

2x - y + 5z = 12

A. {(3 - 3t, 2 + t, t)}  

B. {(6 - 3t, 2 + t, t)}  

C. {(5 - 2t, -2 + t, t)} 

D. {(2 - 1t, -4 + t, t)} 

Question 7 of 40        

Use Gaussian elimination to find the complete solution to each system.

            2x + 3y - 5z = 15

x + 2y - z = 4

A. {(6t + 28, -7t - 6, t)}         

B. {(7t + 18, -3t - 7, t)}         

C. {(7t + 19, -1t - 9, t)}         

D. {(4t + 29, -3t - 2, t)}         

Question 8 of 40        

Use Cramer’s Rule to solve the following system.

            3x - 4y = 4

2x + 2y = 12

A. {(3, 1)}     

B. {(4, 2)}      

C. {(5, 1)}      

D. {(2, 1)}     

Question 9 of 40        

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A =                  0

0

1          1

0

  0        0

1

  0       

B =                  0

1

0          0

0

  1        1

0

  0        

A. AB = I; BA = I₃; B = A     

B. AB = I₃; BA = I₃; B = A^-1  

C. AB = I; AB = I₃; B = A^-1   

D. AB = I₃; BA = I₃; A = B^-1  

Both B and D are correct.

Question 10 of 40      

Use Gaussian elimination to find the complete solution to each system.

            x - 3y + z = 1

-2x + y + 3z = -7

x - 4y + 2z = 0

A. {(2t + 4, t + 1, t)} 

B. {(2t + 5, t + 2, t)}  

C. {(1t + 3, t + 2, t)}  

D. {(3t + 3, t + 1, t)} 

Question 11 of 40      

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

            w - 2x - y - 3z = -9

w + x - y = 0

3w + 4x + z = 6

2x - 2y + z = 3

A. {(-1, 2, 1, 1)}        

B. {(-2, 2, 0, 1)}        

C. {(0, 1, 1, 3)}          

D. {(-1, 2, 1, 1)}

Both A and D are same. We w=-1, x =2, y =1 and z =1 is answer.  

Question 12 of 40      

Use Cramer’s Rule to solve the following system.



            x + y = 7

x - y = 3

A. {(7, 2)}     

B. {(8, -2)}    

C. {(5, 2)}      

D. {(9, 3)}     

Question 13 of 40      

Solve the following sys

A. {(-1, -2, 0)}           

B. {(-2, -1, 0)}           

C. {(-5, -3, 0)}           

D. {(-3, 0, 0)}

Equations are missing.

Question 14 of 40      

Use Cramer’s Rule to solve the following system.



            12x + 3y = 15

2x - 3y = 13

A. {(2, -3)}    

B. {(1, 3)}      

C. {(3, -5)}    

D. {(1, -7)}    

Question 15 of 40      

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.

            x + 3y = 0

x + y + z = 1

3x - y - z = 11

A. {(3, -1, -1)}           

B. {(2, -3, -1)}           

C. {(2, -2, -4)}           

D. {(2, 0, -1)}

Question 16 of 40      

Use Cramer’s Rule to solve the following system.



            x + 2y = 3

3x - 4y = 4

A. {(3, 1/5)}  

B. {(5, 1/3)}  

C. {(1, 1/2)}  

D. {(2, 1/2)}  

Question 17 of 40      

Find values for x, y, and z so that the following matrices are equal.

            2x

z            y + 7

4                       =                     -10

6            13

4         

A. x = -7; y = 6; z = 2

B. x = 5; y = -6; z = 2

C. x = -3; y = 4; z = 6

D. x = -5; y = 6; z = 6

Question 18 of 40      

Use Cramer’s Rule to solve the following system.

            x + y + z = 0

2x - y + z = -1

-x + 3y - z = -8

A. {(-1, -3, 7)}           

B. {(-6, -2, 4)}           

C. {(-5, -2, 7)}           

D. {(-4, -1, 7)}           

Question 19 of 40      

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.

            2w + x - y = 3

w - 3x + 2y = -4

3w + x - 3y + z = 1

w + 2x - 4y - z = -2

A. {(1, 3, 2, 1)}         

B. {(1, 4, 3, -1)}        

C. {(1, 5, 1, 1)}          

D. {(-1, 2, -2, 1)}       

Question 20 of 40      

Use Cramer’s Rule to solve the following system.

            x + 2y + 2z = 5

2x + 4y + 7z = 19

-2x - 5y - 2z = 8

A. {(33, -11, 4)}        

B. {(13, 12, -3)}        

C. {(23, -12, 3)}        

D. {(13, -14, 3)}