Solved: Orthonormal Sets in P2 In Exercises 5762, let p(x) = a0 + a1x + a2x2 and q(x) =
Chapter 5, Problem 61(choose chapter or problem)
Orthonormal Sets in \(P_{2}\) In Exercises 57 - 62, let \(p(x)=a_{0}+a_{1} x+a_{2} x^{2}\) and \(q(x)=b_{0}+b_{1} x+b_{2} x^{2}\) be vectors in \(P_{2}\) with \(\langle p, q\rangle=a_{0} b_{0}+a_{1} b_{1}+a_{2} b_{2}\). Determine whether the polynomials form an orthonormal set, and if not, apply the Gram-Schmidt orthonormalization process to form an orthonormal set.
\(\left\{\frac{1+x^{2}}{\sqrt{2}}, \frac{-1+x+x^{2}}{\sqrt{3}}\right\}\)
Text Transcription:
P_2
p(x) = a_0 + a_1 x + a_2 x^2
q(x) = b_0 + b_1 x + b_2 x^2
langle p, q rangle = a_0 b_0 + a_1 b_1 + a_2 b_2
{{1 + x^{2} / sqrt{2}, {- 1 + x + x^{2} / sqrt{3}}
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