how do you solve a matrix equation

Question

[-3 -2] X= [8 -1]

  1 1          6   0

Answer 1

Let A be the 2 x 2 matrix with first row -3  -2 and second row 1  1.

 

Let B be the 2 x 2 matrix  with first row 8  -1 and second row 6 0. 

                                     

 

Then the equation becomes AX = B. To solve this, multiply both sides of the equation (on the left) by A^-1.

 

A ^-1 is the 2 x 2 matrix with first row -1   -2 and second row 1   3.

 

So, A^-1AX = A^-1B.  Therefore, X = A^-1B = 2 x 2 matrix with

 

first row -20   1 and second row 26   -1.