Let u and v be linearly independent vectors in r3 and let p

Question

Question: Let u and v be linearly independent vectors in R³, and let P be the plane through u, v, and 0. The parametric equation of P is x = su + tv (with s, t in R). Show that a linear transformation T : R³ → R³ maps P onto a plane through 0, or onto a line through 0, or onto just the origin in R3. What must be true about T (u) and T (v) in order for the image of the plane P to be a plane?