The result given in Exercise 30b) holds even if all (he eigenvalues of p(λ) are not distinct. Prove this as follows:
(a) Let

and use mathematical induction to prove that
det( Dm(λ)) = (-1)m + αmλm + αm-1λm-1 + ....... + a1λ + ao)
(b) Show that
det(C - λl) = (α n-1 - λ)(-λ)n-1 - det(Dn-2) = p(λ)

Transcribed Image Text:

am am-1a ao -λ 0 0 D,"(A) = 0 0 1 -λ