Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![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](https://content.bartleby.com/qna-images/question/fc05cf68-81ae-4970-8864-261fc4d70f9c/b6b5918d-9c4b-49e9-a621-580b313db577/ijpvu9si_processed.png)
Transcribed Image Text: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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