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2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dr. Define the func- tions fi(x) = 1, f2(x) = x², f3(x) = r³ and let W be the span of fi, f2, and fa- (a) Use the Gram-Schmidt process to find an orthonormal basis for W. (b) Let g(x) = 1+z². Calculate the orthogonal projection of g onto the subspace W.

2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dr. Define the func- tions fi(x) = 1, f2(x) = x², f3(x) = r³ and let W be the span of fi, f2, and fa- (a) Use the Gram-Schmidt process to find an orthonormal basis for W. (b) Let g(x) = 1+z². Calculate the orthogonal projection of g onto the subspace W.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 41E: Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform...
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2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dz. Define the func- tions fi(x) = r, f2(x) = x², f3(x) = r³ and let W be the span of fi, f2, and fa- (a) Use the Gram-Schmidt process to find an orthonormal basis for W. (b) Let g(x) = 1+z². Calculate the orthogonal projection of g onto the subspace W. 2
Transcribed Image Text:2. Equip C[0, 1] with the inner product (f 19) = f(x) g(x) dz. Define the func- tions fi(x) = r, f2(x) = x², f3(x) = r³ and let W be the span of fi, f2, and fa- (a) Use the Gram-Schmidt process to find an orthonormal basis for W. (b) Let g(x) = 1+z². Calculate the orthogonal projection of g onto the subspace W. 2
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