Let S and T be arbitrary nonempty subsets (not necessarily subspaces) of a vector space V and let k be a scalar. The sum S+T' and the scalar product kS are defined by S+T = (u + v : u € S, vɛ T}, AS = {ku : u e S} [We also write w +S for {w} +S.] Let S = {(1, 2), (2,3)}, T = {(1,4), (1,5), (2, 5)}, w = (1, 1), k = 3 Find: (a) S+ T, (b) w +S, (c) kS, (d) kT, (c) kS + kT, (f) k(S+ T').

Let S and T be arbitrary nonempty subsets (not necessarily subspaces) of a vector space V and let k be a scalar. The sum S+T' and the scalar product kS are defined by S+T = (u + v : u € S, vɛ T}, AS = {ku : u e S} [We also write w +S for {w} +S.] Let S = {(1, 2), (2,3)}, T = {(1,4), (1,5), (2, 5)}, w = (1, 1), k = 3 Find: (a) S+ T, (b) w +S, (c) kS, (d) kT, (c) kS + kT, (f) k(S+ T').

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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