Suggest the polynomial p(t) = c0 + c1t + c2t^2 + t^3. The companion matrix of p is the following 3 x 3 matrix:
0 1 0
C(p)= 0 0 1
-c0 -c1 -c2
(a) Show that if lambda is a root of p, then [1 lambda lambda^2] ^T is an eigenvector of C(p). Find the corresponding eigenvalue of this eigenvector.
(b) Show that if p(t) has three distinct roots, then C(p) is diagonalizable.