# How to see if a subspace is contained in another subspace?

So basically I have a problem with 2 subspaces given in the following spans $$U=\mathscr L\{(1,2,-1,3),(2,4,1,-2),(3,6,3,-7)\}$$$$V=\mathscr L\{(1,2,-4,11),(2,4,0,14)\}$$ And I am asked if it is true if U$$\subseteq$$V or V$$\subseteq$$U. I understand the concept of 2 subspace being equal or proving a subset being a subspace of $$\mathbb R^n$$ by checking the sum of the vectors and the multiplication by a constant but I don't believe to understand the procedure to check if one subspace is contained in another one.

If the generators of $$V$$ are in $$U$$, then $$V \subseteq U$$.
EDIT: in this particular case, you can do it faster. Call $$u_1, u_2, u_3$$ the generators of $$U$$. Then $$u_2 - 2u_1 = 2(u_3 - 3u_1)$$, so both $$U$$ and $$V$$ have dimension $$2$$. You just have to check if they are equal or not.