Answered: Let V be a vector space over F and let…

Let V be a vector space over F and let f : V → F be a linear transformation. Consider the function T : V → F × V defined by T(v) = (f(v), v). Is T a linear transformation?

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

Let V be a vector space over F and let f : V → F be a linear transformation. Consider the function T : V → F × V defined by T(v) = (f(v), v). Is T a linear transformation?

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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