Find A and B

Solve the equations simultaneously.

We have,

        2A - B = X

and    A + 2B = Y

 

Eliminating matrix B, we get  5A = 2X + Y

                                           = 2[6 -6 0] + [3  2   5]

                                                -4  2 1]    -2 1 -7]

 

                                           = [ 15 -10  5]

                                               -10  5  -5]

Hence A = [ 3  2   1]

                -2  1  -1]

Using equation 1, B = 2A - X = 2[3  2  1 ] - [6  -6  0]

                                            -2  1 -1]    -4  2   1]

                                       

                                       = [ 0  10  2]

                                            0   0 -3]