If $f,g$ are linear forms of a finite dimensional vector $V$ of dimension $n$ that are not proportional then $ker (f) \cap ker (g)$ has dimension $(n-2)$. I showed in previous exercises that
Two linear forms are proportional $ \iff $ they have the same linear subspace (say N) as their kernel.
That linear forms of finite vector spaces have kernel (n-1) dimensional by Rank-Nullity.
Not sure how to proceed. It seems to me that f,g most have different kernels since they are not proportional. Any hints on how to solve this problem appreciated.