Sudarsan Meher Asked a Question
August 14, 2020 8:39 pmpts 30 pts
Example: Let V be the set of all pairs (x, y) of real number, and let F be the field of real no. define (x, y) + (x, y,) = (3y + 3y,, -x - x) c(x, y) = (3cy, cx) S Verify that V, with these operations is not a vector space over the field of real number. Solution: Take a (1, 2), B = (2, 3), y = (1, 3) Then (a +B) +Y = {(1, 2) + (2, 3)} + (1, 3) = (15, -3)+ (1, 3) = (0, -16) a+(B + y) = (1, 2) +{(2, 3) + (1, 3)} = (1, 2) + (18, -3) =(-3, -19) Thus we conclude that in general (a+)+Y a + (+Y)
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  • Anonymous User Best Answer
    see the attachment
    • cropped5044452568404631423.jpg
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  • Anonymous User thankyou
    since the associativity is not satisfied by the vectors in V art addition, therefore V is not abelian group Wrt addition and hence it is not a vector space
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    Sudarsan Meher
    I have a doubt on choosing alfa beta and gama
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