In each of the following cases, decide if the set V with the described operations is a real vector space.
(a) V = {(c, y) ∈ R^2; x ≠0 and y ≠0} with vector addition + and scalar multiplication • defined as
(x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) and a • (x, y) = (ax, ay)
(b) V = R with vector addition + and scalar multiplication • defined as
x + y = x + 2y and a • x = ax
(c) V = R with vector addition + and scalar multiplication • defined as
x + y = x + y + 2 and a • x = ax + 2a - 2