1. ## multilinear algebra problem

Let $w$ a 2-form $\in \Lambda^{k}((\mathbb{R}^{n})^{*})$ with n odd. Prove that there exists nonzero vector $u$ $\in \mathbb{R}^{n}$ such that $w(u, v)=0$ for all $v$ $\in \mathbb{R}^{n}$.

2. ## Re: multilinear algebra problem

Originally Posted by hizocar
Let $w$ a 2-form $\in \Lambda^{k}((\mathbb{R}^{n})^{*})$ with n odd. Prove that there exists nonzero vector $u$ $\in \mathbb{R}^{n}$ such that $w(u, v)=0$ for all $v$ $\in \mathbb{R}^{n}$.
Hint: Think of a particular map $f:\Lambda^2((\mathbb{R}^n)^\ast)\to\mathbb{R}$ for which what you are attempting to prove is equivalent to $\ker f\ne 0$.

3. ## Re: multilinear algebra problem

i tried, but i always end up with the same problem :/