3.Consider the inner product (p, q) = S p(x)q(x) dx on P3. LetU = span{1, x, x²}.(a) Find an orthogonal basis for U.(b) Write r³ as a sum of a vector in U and a vector in U-.(c) Find a basis for U-.

Answered: Image /qna-images/answer/6fecd4a8-17aa-4925-a0b9-2993f778471d.jpg

3. Consider the inner product (p, q) = So p(x)q(x) dx on P3. Let U = span{1,x, x²}. (a) Find an orthogonal basis for U. (b) Write x³ as a sum of a vector in U and a vector in U-. (c) Find a basis for U-.

3. Consider the inner product (p, q) = So p(x)q(x) dx on P3. Let U = span{1,x, x²}. (a) Find an orthogonal basis for U. (b) Write x³ as a sum of a vector in U and a vector in U-. (c) Find a basis for U-.

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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Question

3.
Consider the inner product (p, q) = S p(x)q(x) dx on P3. Let
U = span{1, x, x²}.
(a) Find an orthogonal basis for U.
(b) Write r³ as a sum of a vector in U and a vector in U-.
(c) Find a basis for U-.

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