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, cxx) v

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, CXx) Verify that V, with these operations is not a vector space over the field of real number.