Determine whether the set of all pairs of real numbers of the form (x, y), where x ≥ 0, with the standard operations on R2 is a vector space or not.

Answer 1

No, the set is not a vector space. The set is not closed under scalar multiplication.

For example, (3, -4) is in the set, but -2(3, -4) = (-6, 8) is not.