- Let (-) be the evaluation inner product on P₂ at -1, 0, and 1. That is, for any p = p(x) and q = q (x), wehave (p, q) = p(-1)q(-1) +p(0)q(0) +p(1)q(1). Determine whether or not the set {1+x², x, x + x²}is orthogonal in this inner product.

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Answered: (x), we - Let (-) be the evaluation…

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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(x), we - Let (-) be the evaluation inner product on P₂ at -1, 0, and 1. That is, for any p = p(x) and q = q have (p, q) = p(-1)q(-1) + p(0)q(0) +p(1)q(1). Determine whether or not the set {1+x², x, x+x²} is orthogonal in this inner product.