<Mentor's note: moved from general mathematics to homework. Thus no template.> Prove subspace is only a subset of vector space but not a vector space itself. Even a subspace follows closed under addition or closed under multiplication,however it is not necessary to follow other 8 axioms in vector space. if some subspace follow closed under addition or closed under multiplication but don't follow Distributive axioms of c(x+y) = cx + cy(mean they cannot be added in this way),then it is a subspace but not vector space. thank right?