Let V be the set of vectors in R2 with the following definition of addition and scalar multiplication. Determine which of the Vector Space Axioms are satisfied?
1) A1. x + y = y + x for any x and y in V
2) A2. (x + y) + z = x + (y + z) for any x, y, and z in V
3) A3. There exists an element 0 in V such that x + 0 = x for each x in V
4) A4. For each x in V, there exists an element -x in V such that x + (-x) = 0
5) A5. α * (x + y) = (α * x) + (α * y) for each scalar α and any x and y in V
6) A6. (α + β) * x = (α * x) + (β * x) for any scalars α and β and any x in V
7) A7. (α * β) * x = α * (β * x) for any scalars α and β and any x in V
8) A8. 1 * x = x for all x in V