I am sure this is easy but I have been trying all day and just don't understand the question.
Determine whether the set, together with the indicated operations, is a vector space.
1. The set {(x, -x) : x is a real number} with the standard operations.
2. The set {(x, y) : x, y are a real numbers such that x > y} with the standard operations.
Any help would be appreciated. Thanks