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Transcript
Finite Mathematics and Calculus with Applications
(7th Edition)
by Lial, Greenwell, and Ritchey
Section 2.2- Solution of Linear Systems- Gauss-Jordon Method
3.
Write the augmented matrix for the system
      
       
 
When we write the augmented matrix, we don't write the x, y, and z
and we replace the "equal sign" with a vertical line.
The augmented matrix is
7.
Write the system of equations associated with the augmented matrix
The system of equations is
       or simply   
       or simply   
        or simply    
21.
Use the Gauss-Jordon method to solve the system of equations
    
    
The initial matrix is
Divide the 1st row by 2 .
Add   times the 1st row to the 2nd row.
Note the last row represents the equation       which is
not true for any values of  and  Therefore, the system has
no solution.
33.
Solve the system of equations
      
      
      
We can solve this equation using a graphing calculator. Key in the
matrix

 
  


    forget the vertical line
   

 
Your calculator can reduce this matrix using the rref( ) function.
Note that since the last row is all zeros, one the 3 equations has
dropped out and there are an infinite number of solutions. The
numbers are accurate to 3 decimal places.
Forget the 3rd row and just look at the 1st 2 rows.
The 2nd row             
The 1st row            
The solution to the system is        