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

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

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

Let X = {−1,0,1} and consider the inner product on F(X) defined as follows:

⟨f, g⟩ = f (−1)g(−1) + 2f (0)g(0) + 4f (1)g(1).

Let E be the subspace of all even functions defined on X. Set g(x) = x² + x for every x ∈ X.

Find the orthogonal projection of g onto E.

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