  We prove that, for any $d$ linearly independent functions from some set into
a $d$-dimensional vector space over any field, the family of zero sets of all
non-trivial linear combination of these functions has VC-dimension and
Littlestone dimension $d-1$. Additionally, we characterize when such families
are maximal of VC-dimension $d-1$ and give a sufficient condition for when they
are maximal of Littlestone dimension $d-1$.
