A+ Answers

Question 1     
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 2     
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
            x + y + z = 4
x - y - z = 0
x - y + z = 2
A. {(3, 1, 0)} 
B. {(2, 1, 1)}  
C. {(4, 2, 1)}  
D. {(2, 1, 0)} 
           
Question 3     
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     
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 5     
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 6     
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 7     
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
            2x - y - z = 4
x + y - 5z = -4
x - 2y = 4
A. {(2, -1, 1)}
B. {(-2, -3, 0)}           
C. {(3, -1, 2)}
D. {(3, -1, 0)}
Question 8     
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 9     
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 10   
Use Cramer’s Rule to solve the following system.
            2x = 3y + 2
5x = 51 - 4y
A. {(8, 2)}     
B. {(3, -4)}    
C. {(2, 5)}      
D. {(7, 4)}     
           
Question 11   
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           
Question 12   
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
            5x + 8y - 6z = 14
3x + 4y - 2z = 8
x + 2y - 2z = 3
A. {(-4t + 2, 2t + 1/2, t)}       
B. {(-3t + 1, 5t + 1/3, t)}       
C. {(2t + -2, t + 1/2, t)}         
D. {(-2t + 2, 2t + 1/2, t)}       
           
Question 13   
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 14   
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 15   
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 16   
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
            x - 2y + z = 0
y - 3z = -1
2y + 5z = -2
A. {(-1, -2, 0)}           
B. {(-2, -1, 0)}           
C. {(-5, -3, 0)}           
D. {(-3, 0, 0)}
Question 17   
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 18   
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 19   
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 20   
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
            x + y - z = -2
2x - y + z = 5
-x + 2y + 2z = 1
A. {(0, -1, -2)}           
B. {(2, 0, 2)}  
C. {(1, -1, 2)}
D. {(4, -1, 3)}