Let V denote the set of ordered pairs of real numbers. If (a1, az) and (b1, b2) are elements of V and c e R, define (а,а2) + (b1,bz) %3 (а, + b,azbz) and c(a, a2) %3D (са, а2). Is V a vector space over R with these operations? Justify your answer

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13) Let V denote the set of ordered pairs of real numbers. If (a,, az) and (b1, b2) are elements of
V and c E R, define
(a1, a2) + (b1, b2) = (a1 + b1, azb2) and c(a1, a2) = (ca,, a2).
Is V a vector space over R with these operations? Justify your answer
Transcribed Image Text:13) Let V denote the set of ordered pairs of real numbers. If (a,, az) and (b1, b2) are elements of V and c E R, define (a1, a2) + (b1, b2) = (a1 + b1, azb2) and c(a1, a2) = (ca,, a2). Is V a vector space over R with these operations? Justify your answer
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