Please solve on Matlab and by hand when noted otherwise.

2. (Cayley-Hamilton Theorem, 13pt ) You are given the matrix A=[1077;402720;26169] a) [2pt] Find the characteristic polynomial p() of A. Hint: use Matlab, write down the polynomial explicitly. b) [4pt] Evaluate p(A), that is, plug the matrix into its own characteristic polynomial. Hint: you can use polyvalm, if you don't, be sure you implement the constant term right. Hint 2: the result should be notable. The fact that this is always the case is the CayleyHamilton theorem. c) [4p] Write down the matrix equation you get in b). Isolate I on one side and factor out A on the other side (so the resulting equation should look like I=A() ). Show the result. d) [3pt] Use your work from c) to compute the inverse of A without using any of the built-in inverse methods, or rref, etc. Just using the matrix algebra you did in part c). Check your result