Section 4.5: Solving a Linear System


We can uses matrices to solve linear equations!!!
assuming that 2 linear equations are given that  both have x, y and 
product values will enable us to solve our problem.  
For this example:
The matrix A is the coefficient matrix of the system.  
X is the matrix of variables, and B is the matrix of constants.

ex. 1  Solve for these equations:

 2x - 3y = 10
-5x + 8y = -26

begin by writing the equation in matrix form (look back to section 1 for help on this!)


  = 

Then, find the inverse for matrix A




Finally, multiply the constant matrix, (the products) by the 
inverse of the coefficient (matrix A).

 =  = 

The Solution of the system is x=2 and y= -2 



You try:

1)	Write the linear system as a matrix equation:

 2x - 4y = 7
-3x +  y = 12

2)	Use an inverse matrix to solve the linear system:

-2x - 3y = -25
 3x + 4y = 36







Answers:

1)
 	=   


2)	
x = 8
y = 3