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Section 5 By:Erica Wilson

  •    A linear system can be written as a MATRIX EQUATION AX=B.
Example:
        [5  -4]   *   [x]    =  [8]  ------> 5x-4y=8
        [1   2]   *   [y]    =  [6]  ------> 1x+2y=6
  •  When solving for AX=B, you can not divide matrices, but we can multiply them by the inverse. 
    • A^-1 AX=B * A^-1
    • ix= B * A^-1    
    •  x=B * A^-1
Example:
          -x + 3y +5z = -15                                            
          2x + y = 1                                                                              
        -9x - 8y -4z =12                                                                      

Step 1: change the equations into matrices.

A:                                                            B:
  

                       

 

Step 2: Find the inverse of A and multiply by B

A^-1*B

 

Step 3: Solve the Equation.

                                 ANSWER

                       
 
                     
Step 4. Rewrite

  (4,-7,2)

 
 
 
 
 

 

 
 
 
 Click here for more examples
 
 
 
Click here to watch the Section 5 video.