be the set of polynomials of degree at most 3 in R. That is, P3(R) = {ao + a1x + a2x² + a3x° | aj € R} ine which of the following are subspaces of P3(R). Justify your ans - {p(x) € P3 (R) | p'(5) = p'(7)}

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3. Let P3(R) be the set of polynomials of degree at most 3 in R. That is,
P3(R) = {ao + ajx + a2x² + azx³ | a; e R}
Determine which of the following are subspaces of P3(R). Justify your answer.
1. U = {p(x) € P3 (R) | p'(5) = p'(7)}
2. U = {p(x) E P3 (R) | p'(5) = 1}
Transcribed Image Text:3. Let P3(R) be the set of polynomials of degree at most 3 in R. That is, P3(R) = {ao + ajx + a2x² + azx³ | a; e R} Determine which of the following are subspaces of P3(R). Justify your answer. 1. U = {p(x) € P3 (R) | p'(5) = p'(7)} 2. U = {p(x) E P3 (R) | p'(5) = 1}
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