Hi,

**problem:**
Prove that if y is a linear functional on an n-dimensional vector space V, then the set of all those vectors x for which [x,y]=0 is a subspace of V; what is the dimension of that subspace?

**attempt:**
Let X be the set of vectors x in V for which [x,y]=0 where y is a linear functional. Let $\displaystyle x_1\;and\;x_2$ be any two vectors in X and let $\displaystyle \alpha\;and\;\beta$ be arbitrary scalars. Then,

$\displaystyle [\alpha x_1+\beta x_2,y]=\alpha[x_1,y]+\beta[x_2,y]=0 $ and so X is a subspace of V.

Don't know the dimension, maybe n-1

Thanks!