Let W = Linin (1)-(²)) and U-Lim (2)U=(a) Show that R³ = WOU. Explain.(b) Find matrix P that represents a projection of R³ on W parallel to U.(c) Find vector u EU that will be closest to the vector z = 1(d) Find an orthonormal basis of W and extend it to the orthonormal basis of R³.

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Answered: Let W = Lin and U= Lin 2 (a) Show that…

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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Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.