The equivalent condition for a skew-symmetric bilinear form on a finite dim vector space to have rank 2

Question

Let V be a finite dimensional vector space over a subfield of $\Bbb C$ and $f$ a skew-symmetric bilinear form on V. I was trying to show that $f$ has rank 2 if and only if there exist linearly independent linear functionals $L_{1} ,L_{2}$ on V such that $$f(u,v) = L_{1}(u) L_{2}(v) – L_{1}(v) L_{2}(u) , \forall u,v \in V$$ I have been able to prove that $f$ has rank 2 implies there exist linearly independent linear functionals $L_{1} ,L_{2}$ on V . But unable to prove the other side, please help me.