Let V be the vector space P(t) of all polynomials in t over R, with inner product defined by(f(t), g(t)) = S, f(t)g(t) dt. Let W be the subspace P2(t) of V.(a) Show that B(b) Find the projection of f(t) = t³ onto W.{1, 2t – 1,6t? –- 6t + 1} is an orthogonal basis for W.|

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Answered: Let V be the vector space P(t) of all…

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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TRUE or FALSE: If C = {u1,..., u,} is an orthonormal basis for a subspace H of R", and if y is a vector in H, then the coordinate vector of y with y ui y· u2 respect to the basis C is givén by [y]c = y up

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Let V be the vector space P(t) of all polynomials in t over R, with inner product defined by (f(t), g(t)) = S f(t)g(t) dt. Let W be the subspace P2(t) of V. (a) Show that B = {1,2t – 1, 6t² – 6t + 1} is an orthogonal basis for W. (b) Find the projection of f(t) = t³ onto W.