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Problem 4. Let U be the subspace of P4 (R) defined as 1 = {p(x) = 1 € P₁(R) : [ p(x) dx = (a) Find a basis of U. P(0)}. p(x) dx = p(0) (b) Extend the basis in part (a) to a basis of P4(R) (c) Find a subspace W of P4 (R) such that P₁(R) = U + W.

Problem 4. Let U be the subspace of P4 (R) defined as 1 = {p(x) = 1 € P₁(R) : [ p(x) dx = (a) Find a basis of U. P(0)}. p(x) dx = p(0) (b) Extend the basis in part (a) to a basis of P4(R) (c) Find a subspace W of P4 (R) such that P₁(R) = U + W.

Advanced Engineering Mathematics
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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Problem 4. Let U be the subspace of P₁ (R) defined as (a) Find a basis of U. U J = {p(x) € P₁ (R) = [ { p(x)dx = p(0}} : P(0)}. -1 (b) Extend the basis in part (a) to a basis of P4(R) (c) Find a subspace W of P₁(R) such that P₁(R) = U º W.
Transcribed Image Text:Problem 4. Let U be the subspace of P₁ (R) defined as (a) Find a basis of U. U J = {p(x) € P₁ (R) = [ { p(x)dx = p(0}} : P(0)}. -1 (b) Extend the basis in part (a) to a basis of P4(R) (c) Find a subspace W of P₁(R) such that P₁(R) = U º W.
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