The blue subset W of R^2 of all points (x,y) with x>=0, y>=0 is not a subspace of R^2. It is not closed under scalar multiplication: alpha (x,y) not in W for alpha < 0. W is also not closed under addition (e.g. if the gray v-u is in one of the other three black quadrants.) [Anton+Rorres, Elementary Lin. Alg. Appl. Version, Example 3, p. 212.]

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