Subspace Test

When given a set $W$ that is a Subset of Vector Space $S$

1. $\vec{0}\in W$
2. S is Closed Under Addition ($\vec{x},\vec{y}\in W⟹\vec{x}+\vec{y}\in W$ )
3. S is Closed Under Scalar Multiplication ($\vec{x}\in S,k\in R⟹k\vec{x}\in W$) Or, you could group it to be:
4. $\overrightarrow{0}\in W$
5. $\overrightarrow{x},\overrightarrow{y}\in W⟹\overrightarrow{x}+\overrightarrow{y}\in W$