For $T\in\wedge^{k} V^{\ast}$ the annihilator is set $$an(T)= \{\phi\in V^{\ast}\mid \phi\wedge T=0\}$$
Then I need to prove that $dim(an(T))\leq k$ and is equal iff $T$ is decomposable ($i.e.$, $T=\phi_1\wedge\cdots \wedge \phi_k$ for $\phi_j \in V^{\ast}$).
I do not know how to attack this problem, suppose that has dimension greater that $k$ but I get no contradiction or at least do not know how to find it.