EX-let d'be ametric on a vector space X inducedfrom a norm hx and d defind byaSlab)= {od (a,if a = b(a,b)+is abShow that cannot be induced froman normon X.2) let à be trivel metric show that I cannotbe induced from an norm on X-3) let M be closed subspace of anormed spacexConstruct the space X/Mas a normed space.4) let Mix be vector space of 2x3 matrices on Rwrite with Prove convex set and hyper Plane of M5) show that every a finite dimension subspace ofanormed space is closed.

Problem 1: Show that d' cannot be induced from a norm on XThe metric d' is defined as:d'(a,b) = 0 if…

Answered: EX-let d'be ametric on a vector space X…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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