matrix

Note that we have this matrix equation :

Ax  = b        where A =   [5  -2             and     b = [ 2

                                        2  -1]                             -4]                       

If I multiply both sides of the equation [on the left] by the inverse of A, we have

(A^-1) (A )x  =( A^-1 ) b

But    (A^-1) (A)  is just the Identity matrix,  I

So.....the left side just simplifies to  x .......and we have

x = A^-1 b

So.....we just   need to find the inverse of A  = A^-1

Note, for a 2 x 2 matrix  in the form of      [ a     b

                                                                   c     d ]

The inverse is given by :    [1/ (ad - bc)] *  [  d   - b    =

                                                                    - c    a]

[1 / (-5 +4)] * [ -1  2     =     [-1] [ -1  2

                        -2  5]                   -2  5]

So.....the inverse of A   =  [1    - 2    

                                           2    -5]  

So......

x = A^-1 * b     =     [ 1    - 2   *    [2             =          

                              2    -5 ]       -4]                  

   [1*2  +    -2*-4      =    [ 2 +8        =  [10

    2*2  +  - 5* -4 ]           4 +20]           24]

So....the last matrix is the answer.......

And that's it !!!!