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.
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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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 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.
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