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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
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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Shashi ranjan sinha![best-answer]()
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
I have a doubt on choosing alfa beta and gama
see.... u can choose any vectors in place of the vectors chosen for alpha, beta ,gamma.....but in the given solution,it has been so chosen in order to show that associativity is not satisfied