1) Let B =be an orthogonal basis, y =and let W = span(B).A) Calculate the orthogonal projection of y onto W using two different methods.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+b and |lc||= |la|P + ||b||, but neither a nor bare orthogonal projections of c onto W.

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1) Let B = be an orthogonal basis, y = and let W = span(B). %3! 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. E C) Let a = Show c = a+band ||c|? = ||a||? + ||b||², but neither a nor b and c = %3D are orthogonal projections of c onto W.E

1) Let B = be an orthogonal basis, y = and let W = span(B). %3! 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. E C) Let a = Show c = a+band ||c|? = ||a||? + ||b||², but neither a nor b and c = %3D are orthogonal projections of c onto W.E

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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