1. The problem statement, all variables and given/known data Let V denote the set of ordered pairs of real numbers. If (x, y) and (w, z) are elements of V and a is a real scalar, define (x, y) + (w, z) = (x + w, yz) and a(x, y) = (ax, y). Is V a vector space? 2. Relevant equations 3. The attempt at a solution Going through the vector space axioms everything is fine until we need to show that a zero vector exists. Specifically, it is clearly evident that no such zero vector exists. However, how do we prove that no such zero vector exists, and hence it is not a vector space? For example, we can easily show that (0, 0) and (1, 1) do not work. However, this does not show that now pair will work (although clearly no pair will work).