I'm stuck on a relation issue if there is a direct relation at all. If I were to verify that a subset is a subspace of a vector space V, would it then be correct to check that subset for linear independence to verify that the subset spans the subspace? I'm not sure if I'm following the material quiet correctly. I completely understand that if the set is linearly independent it is a basis for V and that if S spans V it is a basis, but I'm unsure of the process connection to any verification of a subspace. Thank you.