Take a look at this here:

sage: A = matrix(QQ, 3, [0,1,2,1,1,3,-1,0,-1])
sage: A

[ 0  1  2]
[ 1  1  3]
[-1  0 -1]
sage: A.kernel()

Vector space of degree 3 and dimension 1 over Rational Field
Basis matrix:
[ 1 -1 -1]
sage:

Perhaps I'm just completely dumb but this vector is not contained in
the kernel of A.

My SAGE version is:
sage: version()
'SAGE Version 3.0, Release Date: 2008-04-21'

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