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The set of all ordered pairs (x.y) with the operations (x,,y.)+(x2,Y2)=(x, + y2, Y +X2) and k(x, y)= (kx, ky) is not a vector

The set of all ordered pairs (x.y) with the operations (x,,y.)+(x2,Y2)=(x, + y2, Y +X2) and k(x, y)= (kx, ky) is not a vector space.

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