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cookiesyum
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Homework Statement
Let P2 denote the space of polynomials in k[x] and degree < or = 2. Let f, g exist in P2 such that
f(x) = a2x^2 + a1x + a0
g(x) = b2x^2 + b1x + b0
Define
<f, g> = a0b0 + a1b1 + a2b2
Let f1, f2, f3, f4 be given as below
f1 = x^2 + 3
f2 = 1 - x
f3 = 2x^2 + x + 1
f4 = x + 1
Find an orthogonal basis of Span(f1, f2, f3, f4).
Homework Equations
Gram-Schmidt orthogonalization process.
The Attempt at a Solution
Span(f1, f2, f3, f4) = Span(w1, w2, w3, w4)
Take S = {f, 1}
w1 = f1
w2 = 1 - (<1, f1>/<f1, f1>)*f1
w3 = 1 - (<1, f2>/<f2, f2>)*f2 - (<1, f1>/<f1, f1>)*f1
w4 = 1 - (<1, f3>/<f3, f3>)*f3 - (<1, f2>/<f2, f2>)*f2 - (<1, f1>/<f1, f1>)*f1
Is this the correct procedure? Can I take g = 1 like that?
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