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Elementary Linear Algebra (MindTap Course List)

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 16CM

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Question

Which of the following mappings are linear transformations? Give a proof (directly using the
definition of a linear transformation) or a counterexample in each case. [Recall that PÂ(F) is the
vector space of all real polynomials p(x) of degree at most n with values in F.]
• (-)-(~`.).
=
3y z
(ii) : P₂(F) → P4(F) given by o(p(x)) = p(x²) (so o(ax²+bx+c) = ax + bx² + c).
(i) 0 : R³ → R² given by 0

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