1. Let V = {(x, y) | x,y ER}. Consider the operations "addition" and "scalar multipli- cation" defined by: VxV→V, ((₁, ₁), (2, 2)) → (11.₁) (2, 2) = (₁ +2₂+1, 31 +92) RXV V, (c, (x, y))→co (r₁, y) = (cri+c-1, cy₁). Prove that V with these operations is a vector space over R.

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A: The solution is given as

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