Let u and v be linearly independent vectors in, and let P be the plane through u,

Question:

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