How to determine this?

Question

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

Isn't it just two criteria - 1.ability to sum and the result be in

the set, and 2. ability to multiply by constant and result be

in the set.

since the constant can be negative the result

would not be in set (now x component<0),

the set is not a vector space.