18. Let V = {(a1, a2): a1, a2 € R}. For (a₁, a2), (b₁,b₂2) € V and c € R,define(a1, a2) + (b1,b2) = (a1 + 2b1, a2 + 3b2) and c(a1, a2) = (ca₁, ca₂).Is V a vector space over R with these operations? Justify your answer.

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Answered: 18. Let V = {(a1, a2): a1, a2 € R}. For…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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18. Let V = {(a1, a2): a1, a2 € R}. For (a₁, a2), (b₁,b₂2) € V and c € R, define (a1, a2) + (b1,b2) = (a1 + 2b1, a2 + 3b2) and c(a1, a2) = (ca₁, ca₂). Is V a vector space over R with these operations? Justify your answer.