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

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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Problem 4. Let U be the subspace of P₁ (R) defined as U J = {p(2) € Pall (a) Find a basis of U. = P₁(R) : [₁ p(x)dx = p(x)dx = p(0) x = p(0)}. (b) Extend the basis in part (a) to a basis of P₁(R) (c) Find a subspace W of P₁ (R) such that P₁ (R) = U + W.
Transcribed Image Text:Problem 4. Let U be the subspace of P₁ (R) defined as U J = {p(2) € Pall (a) Find a basis of U. = P₁(R) : [₁ p(x)dx = p(x)dx = p(0) x = p(0)}. (b) Extend the basis in part (a) to a basis of P₁(R) (c) Find a subspace W of P₁ (R) such that P₁ (R) = U + W.
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