inverse of coefficient matrix

Question

solve the system by first writing the matrix equation, then using the inverse of the coefficient matrix:

 

-4x-3y = -4

6x+5y = 8

Answer 1

To write a matrix equation, separate the coefficients into their own matrix, the variables into their own matrix, and then the answers into their own matrix.

 

In this case, the matrix equation would be:

 

[-4 -3]  [x]    [-4]

[6   5]   [y] =[8]

 

(Note: imagine the two lines together as single matrices)

 

To solve using the inverse matrix, you'd calculate the inverse of the coefficient matrix and multiply it by the answer matrix.

 

[-4 -3]-1               [5    3]

[6 5]       =  (-1/2) [-6  -4]

 

Therefore,

 

[x]            [5    3] [-4]               [4]     [-2]

[y]=(-1/2) [-6  -4] [8]  = (-1/2) [-8] = [4]

 

Therefore, x = -2 and y = 4.