Each of the given sets below is not a subspace because at least one of the 3 properties of being a subspace is failing. • Property 1: the zero vector belongs to the set. • Property 2: the set is closed under vector addition. • Property 3: the set is closed under scalar multiplication. In each case indicate the number of the first condition that is not satisfied, starting checking from condition 1 For example, if a set contains the zero vector but it is not closed under vector addition , you should fill in 2 (because the first condition that is not satisfied is condition 2.) wi (a) W = w2 E R : wi = w2 } is not a subspace and the first property to fail is property 2 {E] Wi (b) W : E R : wi <0, w2 2 0 } is not a subspace and the first property to fail is property w2

Each of the given sets below is not a subspace because at least one of the 3 properties of being a subspace is failing. • Property 1: the zero vector belongs to the set. • Property 2: the set is closed under vector addition. • Property 3: the set is closed under scalar multiplication. In each case indicate the number of the first condition that is not satisfied, starting checking from condition 1 For example, if a set contains the zero vector but it is not closed under vector addition , you should fill in 2 (because the first condition that is not satisfied is condition 2.) wi (a) W = w2 E R : wi = w2 } is not a subspace and the first property to fail is property 2 {E] Wi (b) W : E R : wi <0, w2 2 0 } is not a subspace and the first property to fail is property w2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 43EQ

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