5 8 16 Let A = 4 1 8 4 -4-11 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A and their algebraic multiplicities. (c) For each distinct eigenvalue A of A, find a basis for the X-eigenspace of A. [Hint: If you made a mistake in either (a) or (b), you will find this out here. If you find that one of your eigenspaces is {0}, go back and fix your work in (a) (or (b))!]. (d) Find a matrix P and a matrix D such that P-¹AP = D. [Hint: You do not have to find the inverse of P! Note that you can check your work by checking that AP = PD.]