Example: let v be the set of all pairs (x, y) of real number, and let f be the field of real no. (x y)+(x, y,)= (3y + 3y,,-x- x,) cx, y)= (3cy, - cx) verify tha

Example: Let V be the set of all pairs (x, y) of real number, and let F be the field of real no. (x y)+(X, Y,)= (3y + 3y,,-x- x,) cx, y)= (3cy, - cx) Verify that V, with these operations is not a vector space over the field of real number Solution: Take a = (1, 2), p = (2, 3), y = (1, 3) Then (a+B)+7 = {(1, 2) + (2, 3)) + (1, 3) = (15,-3)+ (1, 3) = (0, -16) a+ (B+ ) = (1, 2) + {(2, 3) + (1, 3)) = (1, 2)+ (18, -3)= (-3, -19) Thus we conclude that in general 1)इस que मे 3 vector क्यू consider किये aur associativity property ही kyu check किये. 2) दुसरी method bhi btao