(a) Let {v1, v2, v3} be a set of vectors that is linearly dependent. Show that for any other vector w, the larger set {v1, v2, v3, w} is also linearly dependent.
(b) Give a list of four distinct vectors in R4 with entries 0, ±1, in any combination, such that the first three form a set that is linearly independent, but the set of all four together gives a set of linearly dependent vectors. You should demonstrate with an equation why the set of four vectors is linearly dependent.