Determine whether the set together with the indicated operat

Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the ten vector space axioms that fails. The set {(x, y): x greaterthanorequalto 0, y is a real number} with the standard operations in R^2.

Solution

No this set does not form vector space.

Additive inverse of each element does not exists.