Let $\omega\in \Lambda^nV$ be an $n$-form for some real linear space $V$. It is known that for $v_1, \dots,v_n\in V$:
$$\omega(v_1,\dots,v_n)=0\iff \{v_1, \dots,v_n\} \ \text{is linearly dependent.}$$
The $\Leftarrow$ implication is easily done. I am, however, having trouble proving $\Rightarrow$.
Can anyone give either a hint or the proof.