Let V = C([0,1]) with the inner product. (f,g) = /J f(t)g(t) dt. Let W be the subspace

Chapter 6, Problem 22

(choose chapter or problem)

Let V = C([0,1]) with the inner product. (f,g) = /J f(t)g(t) dt. Let W be the subspace spanned by the linearly independent set {/, \/t}. (a) Find an orthonormal basis for W. (b) Let h(t) = t2 . Use the orthonormal basis obtained in (a) to obtain the "best" (closest) approximation of //. in W.

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