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?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 10E: Finding the Kernel of a Linear Transformation In Exercises 1-10, find the kernel of the linear...

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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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