octave:40> m1
m1 =

   1   1
   0   0

octave:41> m2
m2 =

   0   1
   3   1

octave:42> m3
m3 =

  -1   0
   1  -1

octave:43> m4
m4 =

   0   2
  -2   2

octave:44> mall = [1 1 0 0; 0 1 3 1; -1 0 1 -1; 0 2 -2 2]'
mall =

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

octave:45> maug = [mall [1 0 0 0]']
maug =

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

octave:46> rref (maug)
ans =

   1.00000   0.00000   0.00000   0.00000   0.50000
   0.00000   1.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   1.00000   0.00000  -0.50000
   0.00000   0.00000   0.00000   1.00000  -0.25000

octave:47> 0.5*m1 - 0.5*m3 - 0.25*m4
ans =

   1   0
   0   0