Subspace test

Given a vector space $(V,+,\cdot )$ a subset $U\subseteq V\}$ is a subspace iff:

1. $0_V\in U$
2. $\mathrm{\forall }{u}_i\in U$ $u_1+u_2\in U$
3. $\mathrm{\forall }c\in \mathbb{R},\mathrm{\forall }u\in U,c\cdot u\in U$

The rest follows from being in a vector space axioms