1. The problem statement, all variables and given/known data Determine if the following set is a vector space under the given operations. List all the axioms that fail to hold. The set of all pairs of real numbers of the form (x,y), where x >= 0, with the standard operations on R^2 2. Relevant equations 3. The attempt at a solution By the axioms of a vector space the set fail on hold this axiom: for each u in V, there is an object -u in V, called negative of u, such that u + (-u) = (-u) + u = 0. If the x term in the pair (x,y) is positive (or zero) then -u = (-x, -y) can not exists. Thus, the negative of u does not exist, and V is not a vector space. Is this correct?