>>% octave
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octave:1> A=[2 -2 -2 -2; -4 0 -2 -6; 2 1 3 3 ; 2 3 3 7]
A =

   2  -2  -2  -2
  -4   0  -2  -6
   2   1   3   3
   2   3   3   7

octave:2> eig(A)
ans =

   4.0000
   4.0000
   2.0000
   2.0000

octave:3> rref(A-2*eye(4))
ans =

   1   0   0   1
   0   1   1   1
   0   0   0   0
   0   0   0   0

octave:4> eye(4)
ans =

Diagonal Matrix

   1   0   0   0
   0   1   0   0
   0   0   1   0
   0   0   0   1

octave:5> rref(A-4*eye(4))
ans =

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

octave:6> rref((A-4*eye(4))^2)
ans =

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

octave:7>(A-4*eye(4))*[-1 0 0 1]'
ans =

   0
  -2
   1
   1

octave:8> (A-4*eye(4))*ans
ans =

   0
   0
   0
   0

octave:9> quit