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2. Suppose {(x), 0₁(x), ..., n(x)} is an orthogonal set of functions with respect to the L2 inner product, i.e. ·b (@₂1 (4) = ["@₂ Prove the Pythagorean theorem þj(x)þk (x)dx = 0, if j = k. ||0o + 1 + ... n ||² = ||00||² + ||1||² + ….. ||n||², where ||f||² = (f, f).

2. Suppose {(x), 0₁(x), ..., n(x)} is an orthogonal set of functions with respect to the L2 inner product, i.e. ·b (@₂1 (4) = ["@₂ Prove the Pythagorean theorem þj(x)þk (x)dx = 0, if j = k. ||0o + 1 + ... n ||² = ||00||² + ||1||² + ….. ||n||², where ||f||² = (f, f).

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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math —— Numerical analysis problems

2. Suppose {(x), 01(x), ..., n (x)} is an orthogonal set of functions with respect to the L2 inner product, i.e. (øj, Øk} = * •;(x)ox(x)dx = 0, _ifj‡k. (6) a Prove the Pythagorean theorem ||¢o + 61 + . . . Ón ||² = ||00||² + ||01||² + . where ||f||2 = (f, f). ||ƒ||² ... ||n||²,
Transcribed Image Text:2. Suppose {(x), 01(x), ..., n (x)} is an orthogonal set of functions with respect to the L2 inner product, i.e. (øj, Øk} = * •;(x)ox(x)dx = 0, _ifj‡k. (6) a Prove the Pythagorean theorem ||¢o + 61 + . . . Ón ||² = ||00||² + ||01||² + . where ||f||2 = (f, f). ||ƒ||² ... ||n||²,
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