Consider the following maps of polynomials S:P →P and T:P→P defined by S(g(x)) = 4 g (5) – g'(-2)and T(g)= -3 g (x)* – 4g' (x). Explain why one these maps is a linear transformation and why the other map is not.
Consider the following maps of polynomials S:P →P and T:P→P defined by S(g(x)) = 4 g (5) – g'(-2)and T(g)= -3 g (x)* – 4g' (x). Explain why one these maps is a linear transformation and why the other map is 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 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
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The one that is a Linear Transformation must be shown using
![A1.
Consider the following maps of polynomials S :P → P and T:P→P defined by
S(g(x)) = 4 g (5) – g' (–2)and T(g)= -3 g (x)³ – 4g' (x).
Explain why one these maps is a linear transformation and why the other map is not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a896025-13d0-489b-adc9-08d570ce0bd7%2F226a7b9a-5aa3-4aea-a994-cfc3e40e5e97%2Fgrijw1_processed.png&w=3840&q=75)
Transcribed Image Text:A1.
Consider the following maps of polynomials S :P → P and T:P→P defined by
S(g(x)) = 4 g (5) – g' (–2)and T(g)= -3 g (x)³ – 4g' (x).
Explain why one these maps is a linear transformation and why the other map is not.
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