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

(a) True. (b) False.

(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, $$v+(-v)=0.$$