7. 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.

7. 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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 25E: 25. Let, where and are non empty, and let and be subsets of . Prove that. Prove that. Prove...

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Q7 Write on paper and write the question too so I can print. Will upvote if correct and done. Thanks a lot.

7. 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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