a) Let V = P3 (R), with an inner product (f.g) = f f(x) g(x) dx. Then for a basis a = {1,x,x², x³), find the matrix representation of an inner product. b) Use Gram-Schmidt orthogonalization process on R4 to convert the basis ((0,1,1,0),(-1,1,0,0), (1,2,0,-1),(-1,0,0,-1)} into an orthonormal basis.

a) Let V = P3 (R), with an inner product (f.g) = f f(x) g(x) dx. Then for a basis a = {1,x,x², x³), find the matrix representation of an inner product. b) Use Gram-Schmidt orthogonalization process on R4 to convert the basis ((0,1,1,0),(-1,1,0,0), (1,2,0,-1),(-1,0,0,-1)} into an orthonormal basis.

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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