1) Let B = be an orthogonal basis, y= and let W = span(B). %3D A) Calculate the orthogonal projection of y onto W using two different methods. t B) Determine the shortest distance from y to W and the shortest point in W closes to y. C) Let a = and c Show c= a+band |lc||? = |la|l + ||b||, but neither a nor b %3D are orthogonal projections of c onto W.
1) Let B = be an orthogonal basis, y= and let W = span(B). %3D A) Calculate the orthogonal projection of y onto W using two different methods. t B) Determine the shortest distance from y to W and the shortest point in W closes to y. C) Let a = and c Show c= a+band |lc||? = |la|l + ||b||, but neither a nor b %3D are orthogonal projections of c onto W.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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