Problem 3 (More vector space properties) Let V be a vector space. Carefully show the following, justi- fying every step of your solution. 1. For every k ER and every u, v EV, we have k(u - v) = ku – kv. 2. For every vector v EV, we have v+v = 2v.

Problem 3 (More vector space properties) Let V be a vector space. Carefully show the following, justi- fying every step of your solution. 1. For every k ER and every u, v EV, we have k(u - v) = ku – kv. 2. For every vector v EV, we have v+v = 2v.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 18EQ

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Problem 3 (More vector space properties) Let V be a vector space. Carefully show the following, justi-
fying every step of your solution.
1. For every k ER and every u, v EV, we have k(u - v) = ku – kv.
2. For every vector v EV, we have v+v = 2v.

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