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18. Let V= {(a1, a2): a1, a2 € R}. For (a₁, a2), (b1,b2) EV 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.

18. Let V= {(a1, a2): a1, a2 € R}. For (a₁, a2), (b1,b2) EV 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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18. Let V = {(a₁, a2): a₁, a2 € R}. For (a₁, a2), (b1,b2) € V and c ER, 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,b2) € V and c ER, 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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