Matlab doesn't allow me to find the base for an eigenspace from rref-form although it gives an eigenvector for an eigenvalue

I have a following matrix for which I first find its eigenvalues:

A=[4,-1,-2,2;-1,3,6,1;-2,6,1,4;2,3,4,-1]
a=eig(A)

After I get the eigenvalues, I try to find the base for the eigenspace for the first eigenvalue a(1) that Matlab gives me (the value is approximately 9.9230). I do the following:

rref([A-a(1)*eye(4), zeros(4,1)])

Matlab returns me an identity matrix with the last column of zeros, suggesting that there are no eigenvectors for that specific eigenvalue. For the other eigenvalues it works normally and lets me deduce the needed bases for the eigenspaces. However, when I use the following

[U,V] = eig(A)

Matlab will indeed give me an example of an eigenvector for the eigenvalue a(1). Hence, there should exist a base for the eigenspace corresponding to that eigenvalue a(1). Could someone please explain, why the rref-form doesn't allow me to deduce the base for the eigenspace? What should I do?

Answer 1

[Matt J]

You should really just do,

null(A-a(1)*eye(4))

But here is what rref gives me,

>> rref([A-a(1)*eye(4), zeros(4,1)])

ans =

    1.0000         0         0    0.5297         0
         0    1.0000         0   -1.7074         0
         0         0    1.0000   -1.7151         0
         0         0         0         0         0

[roamingsleep]

Thank you so much, that's exactly what I was trying find. There must be some kind of a bug on my installed software, for I'm still not able to get those values on my Matlab with the same command...