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Polynomial Linear Operator

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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 polynomials.
f) Exhibit a Jordan basis for P3.

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The calculations for the polynomial linear operator are shown in an attached Word document.

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We have T : P3 -> P3 defined as t (p)(t) = p(t + 1)

a) I claim that T is linear operator. For p,q element of P3, r element of R, we have T ...

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