Please don't use generated AI defined as follows:=Let X {-1,0, 1} and consider the inner product on F(X)(f,g) = f(−1)g(-1)+2ƒ(0)g(0) +4ƒ(1)g(1).Let E be the subspace of all even functions defined on X. Set g(x) = x² + z forevery are X. Find the orthogonal projection of g onto E.

Answered: Image /qna-images/answer/e5cba5c8-66d3-4f6e-ad2b-0238cd5c7c90.jpg

Answered: defined as follows: 1} and consider the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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defined as follows: 1} and consider the inner product on F(X) (f,g) = f(-1)g(-1)+2ƒ(0)g(0) +4ƒ(1)g(1). Let E be the subspace of all even functions defined on X. Set g(x) = x² + for every 2 € X. Find the orthogonal projection of g onto E.