### Polynomial Linear Operator

Let T: P_3 --> P_3 be defined bu (Tp)(t) = p(t + 1). a) Show that T is a linear operator. b) Find the nullspace and range of T. c) Let Beta = (1, 1+t, 1+t+t^2, 1+t+t^2+t^3). Show that Beta is a basis for P_3. d) Find M(T,Beta, Beta). e) Find the eigenvalues and eigenvectors of T and give the characteristic and minimal