Let T : R³ → R² be the linear transformation T(x) = A x' where A = = 246 0 1 0 Find rank(T) and nullity(T). Then determine which of the following properties T satisfies: one-to-one, onto, isomorphism, or none of the above. Explain. Let A be a fixed n x n matrix. For each positive integer k, define the linear transformation Tk : R" → R" by Th(x) = A x for all x ER". Prove that if Ker T = Ker T2, then Ker T³ C Ker T².