Let {x1, x2, . . . , xn} be a basis of a vector space V , n ≥ 2. Show that {x1, x1 + x2, . . . , x1 + x2 + . . . + xn} is also a basis of V . Is the set {x1 + x2, x2 + x3, . . . , xn−1 + xn, xn + x1} a
basis for V too?