= = 12, u₂ (x) = 18x, uz (x) = − 8x²} be a basis for a subspace of P₂. Use the Gram-Schmidt Let {u₁ (x): 1 process to find an orthogonal basis under the integration inner product (ƒ, g) = [₁ f(a)g(x) da on C[0, 1]. 0 Orthogonal basis: {v₁(x) = 12, v₂ (x) = 18x + a, v3(x) = −8x² + bx+c} a = Ex: 1.23 b = Ex: 1.23 c = Ex: 1.23

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let {u₁(x) = 12, u₂(x) = 18x, uz (x) = −8x²} be a basis for a subspace of P2. Use the Gram-Schmidt
process to find an orthogonal basis under the integration inner product (S. 9) =
f(2)g(2) dæ on C[0, 1].
Orthogonal basis: {v₁(x) = 12, v₂ (x) = 18x + a, v3 (x) =
a = Ex: 1.23
b = Ex: 1.23
c = Ex: 1.23
−8x² + bx+c}
Transcribed Image Text:Let {u₁(x) = 12, u₂(x) = 18x, uz (x) = −8x²} be a basis for a subspace of P2. Use the Gram-Schmidt process to find an orthogonal basis under the integration inner product (S. 9) = f(2)g(2) dæ on C[0, 1]. Orthogonal basis: {v₁(x) = 12, v₂ (x) = 18x + a, v3 (x) = a = Ex: 1.23 b = Ex: 1.23 c = Ex: 1.23 −8x² + bx+c}
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