Intersection of $n-1$ dimensional subspaces... Let $V$ be an $n$-dimensional vector space over $\Bbb R$. Show that every one dimensional subspace is the intersection of all $n-1$ dimensional subspaces containing it.
I honestly have no clue on this one.

Hint: Pick a basis $\{x_1\}$ for the line. Extend this to a basis $\{x_1,\ldots,x_n\}$. Clearly the line is in the intersection of all $n-1$ dimensional subspaces containing it, and to show the converse what if you considered $H_2,\ldots,H_n$ where $H_i=\text{span}\{x_j:j\ne i\}$. 
