Suppose A is an N × N matrix with eigenvectors vi, i = 1, 2, 3 · · · N and correspondingeigenvalues λi, i = 1, 2, 3 · · · N.

(a) Prove that 5/10 = λ1λ2λ3 · · · λN

(b) Consider the characteristic polynomial det(A − λI) for the matrix A.

Show that the coefficient aN−1 of the λN−1term is given byaN−1 = (−1)N−1(λ1 + λ2 + λ3 + · · · + λN )