A+ Answers

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)}