(b) Let B = (1, x, x², x³) be the standard basis for cubic polynomials (P3) and define an inner product for f, g € P3 as (f,g) = [*¸ ƒ(x)g(x)dx i. For a non-negative integer k, evaluate the following integral to show that 2 [₁₁2²dx = { 1 + k+1 k even k odd ii. Apply the Gram-Schmidt algorithm on B (in the given order) to find an orthogonal basis C = (ho, h1, h2, h3) for P3.

(b) Let B = (1, x, x², x³) be the standard basis for cubic polynomials (P3) and define an inner product for f, g € P3 as (f,g) = [*¸ ƒ(x)g(x)dx i. For a non-negative integer k, evaluate the following integral to show that 2 [₁₁2²dx = { 1 + k+1 k even k odd ii. Apply the Gram-Schmidt algorithm on B (in the given order) to find an orthogonal basis C = (ho, h1, h2, h3) for P3.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 54E

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