1. The problem statement, all variables and given/known data Prove that if m < n and if y_1,...,y_m are linear functionals on an n-dimensional vector space V, then there exists a non-zero vector x in V such that [x,y_j] = 0 for j = 1,..., m 2. Relevant equations 3. The attempt at a solution My thinking is somehow that we should write every functional in terms of its value at the basis vectors, but well, I'm not really sure what to do. Any help would be nice.