Hi everyone

Stuck on this problem, hoping someone here could point me in the right direction.

We have two subspaces of an inner product space. The dimension of one is larger than the other (and both finite). The question is if there is at least one nonzero vector in the larger subspace that is orthogonal to all vectors of the smaller one.

Clearly this seems to be true for R^{2}and R^{3}but I don't know how to generalize this and in general I just suck at proving things