Show that each of these is not a vector space. (Hìnt. Start by listing two members of each set.) 1. Under the operations inherited from R, this set () {y E R" |a +y+z = 1} 2. Under the operations inherited from R, this set { ER" | + y + = 1} 3. Under the usual matrix operations, (: :) nheeR) 4. Under the usual polynomial operations, {ao + aja + aza* |ao, a1, az € R*} where R* is the set of reals greater than zero

Show that each of these is not a vector space. (Hìnt. Start by listing two members of each set.) 1. Under the operations inherited from R, this set () {y E R" |a +y+z = 1} 2. Under the operations inherited from R, this set { ER" | + y + = 1} 3. Under the usual matrix operations, (: :) nheeR) 4. Under the usual polynomial operations, {ao + aja + aza* |ao, a1, az € R} where R is the set of reals greater than zero

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 33EQ

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