Afat 4Problem 4.Let V {(a1, a2) a₁, a2 in R}; that is, V is the set consisting of allordered pairs (a1, a2), where a₁ and a2 are real numbers. For (a1, a2), (b1,b2) EV and a ER,define(a1, a2)(b₁,b₂) = (a1 + 2b₁, a2 + 3b2) and a(a₁, a2) = (aa₁, αa2).Is V a vector space with these operations? Justify your answer.

Answered: Image /qna-images/answer/f96a6dc3-a3d0-4e13-a1d3-b3011677b852.jpg

4 Problem 4. Let V = {(a1, a2) a1, a2 in R}; that is, V is the set consisting of all ordered pairs (a1, a2), where a₁ and a2 are real numbers. For (a1, a2), (b1,b2) EV and a € R, define (a₁, a2)(b₁,b2) = (a1 + 2b1, a2 +3b2) and a (a₁, a2) = (aa₁, aa2). Is V a vector space with these operations? Justify your answer.

4 Problem 4. Let V = {(a1, a2) a1, a2 in R}; that is, V is the set consisting of all ordered pairs (a1, a2), where a₁ and a2 are real numbers. For (a1, a2), (b1,b2) EV and a € R, define (a₁, a2)(b₁,b2) = (a1 + 2b1, a2 +3b2) and a (a₁, a2) = (aa₁, aa2). Is V a vector space with these operations? Justify your answer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 35E

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