3) Show that the set of all elements of the form (x + 2y,x + 3z, 2x + y + z), where x, y, z E F, is a subspace ofv°(F).

We have, (x+2y , x+3z , 2x+y+z),where x, y, z € F.

Answered: 3) Show that the set of all elements of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 40EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V= F, W=finF:f(0)=1

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In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
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3) Show that the set of all elements of the form (x + 2y,x + 3z, 2x + y + z), where x, y, z E F, is a subspace of v°(F).