Recall that B = {1+2x,3 – x}. Let the vector space P¡ have the inner product (p, q) = 2aobo + 3a¡b¡ where p = ao +a1x and q = bo + b1x. Show that B is an orthogonal basis for P1, but not orthonormal. Transform B into an orthonormal basis for P.
Recall that B = {1+2x,3 – x}. Let the vector space P¡ have the inner product (p, q) = 2aobo + 3a¡b¡ where p = ao +a1x and q = bo + b1x. Show that B is an orthogonal basis for P1, but not orthonormal. Transform B into an orthonormal basis for P.
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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