Which of the following are vector spaces over the scalar field R of real numbers?

A) U = (R x R, +_U, *_U)
where (a₁, a₂) +_U (b₁, b₂) = (a₁ + 2b₁, a₂ + 3b₂)
and *_U is the usual scalar multiplication

B) V = (R x R, +_V, *_V)
where (a₁, a₂) +_V (b₁, b₂) = (a₁ + b₁ + 1, a₂ + b₂)
and *_V is the usual scalar multiplication

C) W = (R x R, +_W, *_W)
where (a₁, a₂) +_W (b₁, b₂) = (a₁ + b₁ + 1, a₂ + b₂ + 1)
and r*_W(a₁, a₂) = (ra₁ + r – 1, ra₂ + r – 1)