Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.1 Vectors in Rn - 4.1 Exercises - Page 154: 51


(a) True. (b) False.

Work Step by Step

(a) True. For any two vectors $u=(u_1,u_2,...,u_n), v=(v_1,v_2,...,v_n)\in R^n$ are equal if and only if their coresponding components are equal, that is, $$u_1=v_1, ..., u_n=v_n.$$ (b) False. $-v$ is the additive inverse and this can be shown from the property of the additive inverse, $$v+(-v)=0.$$
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