I'm having some trouble deciphering the wording of a problem.
I'm given $V$ a vector space over a field $\mathbb{F}$. Letting $v_1$ and $v_2$ be distinct elements of $V$, define the set $L\subseteq V$: $L=\{rv_1+sv_2 | r,s\in \mathbb{F}, r+s=1\}$.
It's the next part where I can't figure out what they mean.
"Let $X$ be a non-empty subset of $V$ which contains all lines through two distinct elements of $X$."
No idea what this set $X$ is. Once I figure that out, I'm supposed to show that it's a coset of some subspace of $V$. I'm hoping this part will become clearer once I know what $X$ is...