Vectors, subsets, and subspaces... Can someone explain this question more simply?

I am having trouble understanding the question, could anyone break it down a little? I learned today about 3 cases that need to be checked, but my notes aren't helping too much.

Is the given subset U of $\displaystyle \mathbb{R}^{4}$ a vector subspace?

a) The set U of all vectors **u** in $\displaystyle \mathbb{R}^{4}$ such that $\displaystyle u_{2}-2u_{3} - u_{4}=0$ and $\displaystyle 3u_{1}+u_{4}=0$

b) The set U of all vectors **u** in $\displaystyle \mathbb{R}^{4}$ such that $\displaystyle u_{2}-2u_{3} - u_{4}=0$ and $\displaystyle 3u_{1}+u_{4}\leq 0$