Let p() = (-1 )n(n - n-1n-1 -....- 1 - o) he a polynomial of degree n I (a) Show that if i, is

Let p(λ) = (-1 )n(λn - αn-1λn-1 -....- α1λ - αo) he a polynomial of degree n ‰¥ I

(a) Show that if λi, is a root of p(λ) = 0 then λi is an elgenvalue of C with eigenvector x = (λin-1,,λ in-2...... λi,1)T ,
(b) Use part (a) to show that if p(λ) has n distinct roots then p(λ) is the characteristic polynomial of C.
The matrix is called the companion matrix of p(λ).

an-1 an-2 a ao 1 00 0