Let a and b be two subspaces of vector space v. show that span of intersection of a and b is contained in the intersection of the span (a) and span (b).

see the attachment

but converse is not true. Take A = { (1,0), (0,1)} and B ={ (-1,0),(0,-1)} . Intersection of A and B is empty and so the subspace spanned by it is zero subspace of R². On the other...