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Three vectors are $(1,0)$, $(-1,2)$, and $(3,1)$. I tried to relate the hull with an affine set, and so a flat. However, I don't find their relation. From what I learn about affine combinations, affine hull of the set is all combinations of the three vectors. That hull may not equal to an affine set, since the hull contains only combination of three vectors, not combinations of the combinations of that vectors. (or at least I cannot prove that). On the other hand, an affine set must contain all combinations

Could anyone help to explain?

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