Let P, be the vector space of polynomials of degree at most 4. (a) Let W1 be the subset of P consists of polynomials p(x) = ao+a1x + azx² + azx³ +a4x4 for which ao + az – a4 = 1. Is W1 a subspace of P,? Justify your answer. (b) Let W, be the subset of P, consists of even polynomials; namely, polynomials p(x) for which p(x) = p(-x). Is W2 a subspace of P4? Justify your answer. (c) Let W3 be the subset of P consists of polynomials p(x) for which p(2) = 2p(3). Is W3 a subsapce of P,? Justify your answer.
Let P, be the vector space of polynomials of degree at most 4. (a) Let W1 be the subset of P consists of polynomials p(x) = ao+a1x + azx² + azx³ +a4x4 for which ao + az – a4 = 1. Is W1 a subspace of P,? Justify your answer. (b) Let W, be the subset of P, consists of even polynomials; namely, polynomials p(x) for which p(x) = p(-x). Is W2 a subspace of P4? Justify your answer. (c) Let W3 be the subset of P consists of polynomials p(x) for which p(2) = 2p(3). Is W3 a subsapce of P,? Justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let P4 be the vector space of polynomials of degree at most 4.
(a) Let W1 be the subset of P consists of polynomials p(x) = ao + a1x + a2x? + azx³ + a4x4
for which ao + az – a4 = 1. Is W1 a subspace of P4? Justify your answer.
(b) Let W, be the subset of P4 consists of even polynomials; namely, polynomials p(x) for
which p(x) = p(-x). Is W2 a subspace of P4? Justify your answer.
(c) Let W3 be the subset of P4 consists of polynomials p(x) for which p(2) = 2p(3). Is W3 a
subsapce of P4? Justify your answer.
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