In P3, define Let W = span(po, P, P2) where po(t) = 1, p (t) =...

 

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In P3, define Let W = span(po, P₁, P2) where po(t) = 1, p₁ (t) = t, p₂(t) = t². a) Find an orthogonal basis for W. <p(x), q (x) >= p(-1)q(-1) + p(0)q(0) + p(1)q(1) + p(2)q(2) b) Find the best approximation to p3 (t) = t³ c) Write p3 (t) as p3 (t) = f(t) + g(t) where f(t)EW and g(t) is orthogonal to W. In P3, define Let W = span(po, P₁, P2) where po(t) = 1, p₁ (t) = t, p₂(t) = t². a) Find an orthogonal basis for W. <p(x), q (x) >= p(-1)q(-1) + p(0)q(0) + p(1)q(1) + p(2)q(2) b) Find the best approximation to p3 (t) = t³ c) Write p3 (t) as p3 (t) = f(t) + g(t) where f(t)EW and g(t) is orthogonal to W.

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In this problem were dealing with an inner product space defined by the inner product p1q1 p0q0 p1q1 ... View the full answer