A vector v = (a,..., an) ER" is called strongly positive if a; > 0 for all i = 1,..., n. a) Suppose that v is strongly positive. Show that any vector that is "close enough" to v is also strongly positive. (Formulate carefully what "close enough" should mean.) b) Prove that if a subspace S of R" contains a strongly positive vector, then S has a basis of strongly positive vectors.