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.

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Chapter7: Eigenvalues And Eigenvectors
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The one that is a Linear Transformation must be shown using Vector addition and Scalar multiplication as proof

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.
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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