Question: Is {(x, y) | x, y R} a vector space under these operations? (a) (x1, y1) + (x2, y2) = (x1 + x2, y1

Is {(x, y) | x, y ∈ R} a vector space under these operations?
(a) (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) and r ∙ (x, y) = (rx, y)
(b) (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) and r ∙ (x, y) = (rx, 0)

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