| Consider a finite set of nonzero vectors, v1, V2, ..., Vk e R", with |v;| > 0, ..., k; k > 1. Define 3. 1, 2 = k C =N Hvi (1) i=1 where we denote H, = {x € R" | v · x < 1}. a. For the set C defined in the above equation (1), is it possible for some case that C = 0? Here, Ø denotes the empty set. Justify your answer, either by giving such a case or proving that it is not possible. b. Give an example of the vectors v; E R?, i = 1,2, 3, (so n = the set C defined in the above equation (1), is a bounded set. Justify your answer clearly. 2 and k = 3) where (Here, a set S is said to be bounded, if there exists a positive number K such that x| < K for any x E S.)

| Consider a finite set of nonzero vectors, v1, V2, ..., Vk e R", with |v;| > 0, ..., k; k > 1. Define 3. 1, 2 = k C =N Hvi (1) i=1 where we denote H, = {x € R" | v · x < 1}. a. For the set C defined in the above equation (1), is it possible for some case that C = 0? Here, Ø denotes the empty set. Justify your answer, either by giving such a case or proving that it is not possible. b. Give an example of the vectors v; E R?, i = 1,2, 3, (so n = the set C defined in the above equation (1), is a bounded set. Justify your answer clearly. 2 and k = 3) where (Here, a set S is said to be bounded, if there exists a positive number K such that x| < K for any x E S.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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