Do all 3 parts There is only one question with 3 parts Don't try to do only ist part I vll devote u LetA =a. By diagonalization of A, compute e4.b. Find ao, a1 so that e4 = aoI + a1A.c. The Cayley-Hamilton theorem: If A is a given n by n matrix with degree n characteristic poly-nomial p(r) = det(A – rI) = (-1)"p" + Cn-1r"-1 + .… + cır + co then A is a root of its owncharacteristic polynomial, i.e. p(A) = (-1)" A" +Cn-1A"-1+..+cA+coI = 0, the zero matriz.Explain using the Cayley-Hamilton theorem why the matrix exponential of an n by n matrix Acan always be expressed as e4 = En ak Ak for some numbers ao, a1,..., an-1.n-1k=D0

Given that A=5-131 Now we have to find eA

Let A = a. By diagonalization of A, compute e^. b. Find ao, a1 so that e4 = aoI+ a1A. c. The Cayley-Hamilton theorem: If A is a given n by n matrix with degree n characteristic poly- nomial p(r) = det(A – rI) = (-1)"r" + Cn-1r"-1 + ..+ cır + co then A is a root of its own characteristic polynomial, i.e. p(A) = (-1)" A" +cn-1A"-1+..+c,A+coI = 0, the zero matriz. Explain using the Cayley-Hamilton theorem why the matrix exponential of an n by n matrix A can always be expressed as e =E ak A* for some numbers ao, a1,..., an-1·