5. The Kernel and Range of a Linear Transformation. (a) [5pts.] 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. (b) [5pts.] Let A be a fixed n ×n matrix. For each positive integer k, define the linear transformation Tk : Rª → Rª by Tk( x¹) = Ak x' for all x' ¤ Rª. Prove that if Ker T = Ker T², then Ker T³ C Ker T².