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Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1) in the vector space P2 of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P2 spanned by the polynomials f(x), g(x) and h(x). { }.

Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1) in the vector space P2 of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P2 spanned by the polynomials f(x), g(x) and h(x). { }.

Advanced Engineering Mathematics
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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Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1) in the vector space P2 of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P2 spanned by the polynomials f(x), g(x) and h(x). { }.
Transcribed Image Text:Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1) in the vector space P2 of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P2 spanned by the polynomials f(x), g(x) and h(x). { }.
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