multilinear algebra problem

**hizocar** · December 18th 2011, 10:01 AM

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 $v$ $\in \mathbb{R}^{n}$ .

**Drexel28** · December 18th 2011, 11:09 AM

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 $\ker f\ne 0$ .

**hizocar** · December 18th 2011, 04:23 PM

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

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