Let V ={(u1,u2,u3)|u3=u1+u2; u1,u2,u3 belong lR} is V subspace of IR^3?
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V is the set of points (u1,u2,u3). The plane containing these points is u1+u2-u3=0, so V is a set of planes in 3-space, which makes V a subspace in real 3-space otherwise represented by R3.

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