Question: The set S = {x1. x2. . . . , xn} is affinely dependent if and only if there exist numbers a1, a2, . .

The set S = {x1. x2. . . . , xn} is affinely dependent if and only if there exist numbers a1, a2, . . . , an, not all zero, such that
a1x1 + a2x2 +...........+ anxn = 0
with a1 + a2 +..........+ an = 0.
Analogous to a basis, every vector in the affine hull of a set has a unique representation as an affine combination of the elements of the set.

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