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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 43E: Prove that in a given vector space V, the zero vector is unique.
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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.
Transcribed Image Text: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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