Question: Let u and v be vectors in Rn. It can be shown that the set P of all points in the parallelogram determined by u and v has the form au + bv, for 0 ≤ a ≤ 1, 0 ≤ b ≤ 1. Let T : Rn → Rm be a linear transformation. Explain why the image of a point in P under the transformation T lies in the parallelogram determined by T (u) and T (v).