Answered: Which of the following subsets of P2…

Which of the following subsets of P2 are subspaces of P2? Explain your answer. If it is a subspace, exhibit a basis. (a) {p(t): p(1) = 2} (b) {p(t): p(2) = 0} (c) {p(t): p(−1) = −p(t)}

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Which of the following subsets of P2 are subspaces of P2? Explain your answer. If it is a subspace, exhibit a basis.
(a) {p(t): p(1) = 2}
(b) {p(t): p(2) = 0}
(c) {p(t): p(−1) = −p(t)}

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