I'm little overshadowed with this problem.
Let $S = (v_1, · · · , v_m) ⊂ V$ be a linearly independent set which spans a non-degenerate subspace W = L(S) and put $W_k = L(v_1, . . . , v_k)$ for every $k = 1, . . . , m$. I have to prove that if one of the vectors in S is lightlike $(v_i)$, it has to exist a second vector $v_j$ such that $g(v_i ,v_j)\ne 0$.
My idea is to use that S is l.i and W is non-degenerate, but I'm a bit lost in this topic. The only thing I know is that $g(v_i,v_i)=0$ . Any help would be appreciated!