Systems Of Equations And Matrices

3.1 Systems of Two Linear Equations in Two Variables
A. Solve the system by graphing (by hand or with Excel)
3x +5y = 46
7x – y = 6
B. Solve the system by graphing (by hand or with Excel)
4x – 5y = 7
2x + 3y = 9
3.2 Matrices and Linear Equations in Two Variables
C. Find the dimensions of the matrix and the values of a2,1 and a3,1
5 9 1 2
3 6 12 4
2 7 3 8
  
 
      
D. Find the dimensions of the matrix and the values of a1,3 and a2,3
7 5 3 4
9 1 14 2
8 6 9 10
   
 

       
E. Write the augmented matrix representing the system of linear equations.
5 7 2
2 3
x y
x y
  
 
F. Write the augmented matrix representing the system of linear equations.
3 5 8
4 5
x y
x y
   
 
G. Carry out the row operation:
2 2
1 1 12 32
2 0 2 16
R R  
    
H. Carry out the row operation:
1 1
1 8 24 32
8 5 22 16
R R  
    
I. Interpret the augmented matrix as the solution of a system of equations. State the solution, or identify the system as
inconsistent or dependent.
1 0 9
0 1 15
     
MAT230 – Finite Analysis
Unit 3 DB: Systems of Equations and Matrices
J. Interpret the augmented matrix as the solution of a system of equations. State the solution, or identify the system as
inconsistent or dependent.
1 0 157
0 1 386
     
K. Solve the system by row-reducing the corresponding augmented matrix.
2 12
3 11
x y
x y
 
 
3.3 Systems of Linear Equations and the Gauss-Jordan Method
L. Find the augmented matrix representing the system of equations:
1 2 3
1 2 3
1 2
2 2
3 4 6
3 1
x x x
x x x
x x x
    
   

   
M. Interpret the row-reduced matrix as the solution of a system of equations:
1 0 0 5
0 1 0 9
0 0 1 2
   
     
N. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix:
1 0 1 15
0 1 0 9
0 0 1 2
   
      
O. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix:
1 0 0 7
0 1 0 16
0 0 2 32
   
     
3.4 Matrix Arithmetic
For problems P – U, use matrices A, B, and C below.
2 3 4 8 7 6 1 6 5
5 6 7 5 4 3 7 2 8
8 9 1 2 1 9 4 9 3
A B C
           
                    
P. Find: A
t
Q. Find: 2B
R. Find: –3C
S. Find: B + C
T. Find: C – A
U. Find: A + 2B
V. Find the matrix product:
2
2 3 1
1
3 1 3
2
  
          
W. Find the matrix product:
2 2
2 3 1
1 4
3 1 3
3 3
            
X. Find the matrix product:
2
4 5 2
3
1 1 3
2
               
Y. Rewrite the system of linear equations as a matrix equation AX = B
1 2 3
1 2 3
1 2 3
2 3 4 1
5 8 6 3
2 3 3 8
x x x
x x x
x x x
    
   

   
Z. Rewrite the system of linear equations as a matrix equation AX = B
1 2 3 4
1 2 3 4
1 2 3 4
2 3 4 5 6
5 8 6 4 1
2 3 3 6 14

Sample Solution