>> A = [1 4 3; -1 -2 0; 2 2 3]

A =

     1     4     3
    -1    -2     0
     2     2     3

>> I = eye(3)

I =

     1     0     0
     0     1     0
     0     0     1

>> B=[A;I]

B =

     1     4     3
    -1    -2     0
     2     2     3
     1     0     0
     0     1     0
     0     0     1

>> B=[A I]

B =

     1     4     3     1     0     0
    -1    -2     0     0     1     0
     2     2     3     0     0     1

>> rref(B)

ans =

    1.0000         0         0   -0.5000   -0.5000    0.5000
         0    1.0000         0    0.2500   -0.2500   -0.2500
         0         0    1.0000    0.1667    0.5000    0.1667

>> inv(A)

ans =

   -0.5000   -0.5000    0.5000
    0.2500   -0.2500   -0.2500
    0.1667    0.5000    0.1667

>> inv(A)*[12 -12 8]
??? Error using ==> *
Inner matrix dimensions must agree.

>> inv(A)*[12; -12; 8]

ans =

    4.0000
    4.0000
   -2.6667

>>