Chapter 4 - Vector Spaces - 4.1 Vectors in Rn - 4.1 Exercises - Page 154: 52

(a) True. (b) False.

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