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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.

(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.

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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- Let (-) be the evaluation inner product on P₂ at -1, 0, and 1. That is, for any p = p(x) and q = q (x), we 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.
Transcribed Image Text:- Let (-) be the evaluation inner product on P₂ at -1, 0, and 1. That is, for any p = p(x) and q = q (x), we 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.
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