(c) Let C be the vector space of continuous real-valued functions on R. IfT: C → C is defined so T(f(x)) = [f(x)], is T a linear transformation? Explain why or why not.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 1CM
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(c) Let C be the vector space of continuous real-valued functions on R. If T: C → C is
defined so T(f(x)) = |ƒ (x)\, is T a linear transformation? Explain why or why not.
Transcribed Image Text:(c) Let C be the vector space of continuous real-valued functions on R. If T: C → C is defined so T(f(x)) = |ƒ (x)\, is T a linear transformation? Explain why or why not.
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