1. Consider the matrix H O A = 3 and the point v = (1, 0, 0). (a) Check that (A - I) 3v = 0 and (A - I)2v # 0. (b) Suppose alv + a2(A - I)v + a3(A - I)2v =0 for some a1, a2, a3 E R. i. Simplify (A - I)(aiv + a2(A - I)v + a3(A - I)2v). ii. Simplify (A - I)2(alv + a2(A - I)v + a3(A - I)2v). iii. What must a1, a2, a3 be? (c) Let B = {(A - I)2v, (A - I)v, v}. Find i. [(A - I)2v] B ii. [(A - I)v]B iii. [v]B (d) Denote the standard basis of R3 by E. For example, (A - I) PEB[(A - I)]B = (A - D)[(A - DuJE = [(A - I)2v]E . Find i. (A - I) PE-B ii. PBLE(A - I) PE--B (e) What is the Jordan Canonical Form of A