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## Homework Statement

Task: Show that U = {(x, y) | xy ≥ 0} is not a subspace of vector space R

^{2}

I wish you could help me to understand why U is not a subspace of R

^{2x2}.

I have actually found a vectors u and v such that it does not belong to U (e.g. (-3,-1) +(2,2) = (-1,1) ) but is that sufficient to show that U is not a subset of R

^{2x2}?