d'p(x) Let U = {p(x) E P3(R) | p"(3) = p"(-5)}, where p"(x) = and p"(x) = dx3 d*p(x) dx? (A) Let p1(x), p2 (x) E U. Show that p1(x) – 4p2(x) E U. (B) Find a basis of U. (C) Extend the basis of U to a basis of P3(R). (D) Find a subspace W of P3(R) such that P3(R) = U + W.

d'p(x) Let U = {p(x) E P3(R) | p"(3) = p"(-5)}, where p"(x) = and p"(x) = dx3 d*p(x) dx? (A) Let p1(x), p2 (x) E U. Show that p1(x) – 4p2(x) E U. (B) Find a basis of U. (C) Extend the basis of U to a basis of P3(R). (D) Find a subspace W of P3(R) such that P3(R) = U + W.

Algebra and Trigonometry (6th Edition)

6th Edition

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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Thank you.

d²p(x)
Let U = {p(x) E P3 (R) | p"(3) = p"(-5)}, where p" (x) =
and p"(x) =
dx2
dp(x)
dx3
(A) Let p1(x), p2(x) E U. Show that p1(x) – 4p2(x) E U.
(B) Find a basis of U.
(C) Extend the basis of U to a basis of P3 (IR).
(D) Find a subspace W of P3 (R) such that P3(R) = U O W.

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