Given the basis vectors of two linear vector spaces, how can I determine if one of the vector spaces is a subspace of the other?

Question

Suppose I know the basis vectors of a linear vector space $X=\{x_i\}$ and another linear vector space $Y=\{y_j\}$. It is not obvious if either of these sets is contained in the other. How can I determine if one of these vector spaces is the subspace of the other?

Answer 1

HINT

A possible way, for a more general result, is to find the basis for each one and find the intersection or, to determine if one is a subspace of the other, consider the RREF to check the linear dependence.