Just (B) pls (a). We assume that {ø1,.., ¢m} C Rd are a set of orthonormal vectors (i.e., ̟ ¢̟ = 1,=t) and let S bethe subspace spanned by {¢1,…., ¢m}. Please show that for any x E Rd,M||r – Psæ|} = min-21,...ZMERk=1and show thatnnM2Ellæ; –Psæ;| =min(zik)ie(n],k€[M]i=1i=1k=1(b). Use the results in (a), show thatnmin x; – Psæ;|} = „minmin ||X – ZV?,-SESMi=1VMEVM ZER" ×Mwhere Vm = {V M = [v1,.., VM] E R¢×M : vJv¿ = 1s=t}.

note : As per the instructions we will only solve part (b). As per the question, we are asked to…

Answered: (b). Use the results in (a), show that…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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(b). Use the results in (a), show that n min|₁ - Psxi||²/2 = SESM i=1 min VMEVM ZERXM min ||X-ZV where VM = {VM = [v₁, ..., UM] € Rd×M : vŢvt = 1s=t}.