I have troubles understanding this whole problem starting at the definition. We have defined the exterior product as follows:
If $\alpha = \pi (a) \in \bigwedge^pV$ and $\beta = \pi(b) \in \bigwedge^q V$, then $$\alpha \wedge \beta = \pi (a\otimes b)$$ Where $\pi: T(V) \rightarrow \bigwedge^\ast V=T(V)/I(V)$ is the quotient projection
I have to show that for finite dimensional $V$ and vectors $v_1, v_2$ it holds that $$v_1 \wedge v_2 = \pi (1/2(u_1 \otimes u_2 - u_2 \otimes u_1))$$
Am I right, by assuming that $v_i=\pi(u_i)$? How do I use this to show this?