6) Suppose that ? is a linear operator on a 2 dimensional vector space ? and that ? = ̸ ? ? for any ? ∈ F. Then if ? ∈ L(V) and ?? = ?? then ? = ?(?) for some polynomial ?(?) (6) Suppose that $ T $ is a linear operator on a 2-dimensional vector space $ V $ and that $ T \neq aI $ for any $ a \in \mathbb{F} $. Then if $ U \in \mathcal{L}(V) $ and $ UT = TU $ then $ U = g(T) $ for some polynomial $ g(x) $.

Answered: Image /qna-images/answer/55dba925-b3a1-475a-933f-e92177dc79c1.jpg

Answered: (6) Suppose that T is a linear operator…

(6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a e F. Then if U E L(V) and UT = TU then U = g(T) for some polynomial g(x).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

6) Suppose that ? is a linear operator on a 2 dimensional vector space ? and that ? = ̸ ? ? for any ? ∈ F. Then if ? ∈ L(V) and ?? = ?? then ? = ?(?) for some polynomial ?(?)

(6) Suppose that $ T $ is a linear operator on a 2-dimensional vector space $ V $ and that $ T \neq aI $ for any $ a \in \mathbb{F} $. Then if $ U \in \mathcal{L}(V) $ and $ UT = TU $ then $ U = g(T) $ for some polynomial $ g(x) $.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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