Find non-trivial solution

[wwfarch@rochester.rr.com]

I'm having an issue with GSL and solving homogeneous systems. In
particular I have an equation of the form:

Av = 0

where A is an Nx6 matrix, v is a vector (size 6) and 0 represents a zero
vector.

Regardless of N when I solve for v I always get the trivial solution (v
= 0). Is there a way to force GSL to provide a non-trivial solution?
Once I have a non-trivial solution I can scale as I need to for my
application. As a note, when N>6 I solve with a least squares solution.
I've tried QR and SVD decompositions.

Thanks,
Matthew Parent