Let V be a vector space and S = {v1, v2, . . . , Un), a subset of vectors of V that spans V. Suppose T is some subset of S that is independent, say the first k vectors of S to fix the notation. i.e. T = {v1, v2, . . . , vx} show that one can add some vectors of S to T to get a basis B of V. In other words, V contains a basis B such that T C B C S