Polynomial Linear Operator
Not what you're looking for?
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.
Purchase this Solution
Solution Summary
The calculations for the polynomial linear operator are shown in an attached Word document.
Solution Preview
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 ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.