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: 52


(a) True. (b) False.

Work Step by Step

(a) True. To subtract two vectors $u=(u_1,u_2,...,u_n), v=(v_1,v_2,...,v_n)\in R^n$ you have to subtract their coresponding components , that is, $$u-v=(u_1-v_1, ..., u_n-v_n).$$ (b) False. $0$ is not the additive inverse but it is the additive identity and this can be shown from the property of the additive identity, $$v+0=v.$$
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