Affine independence

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The set LaTeX:  \{x^0, x^1, \ldots, x^k \} is affinely independent if their affine hull is k-dimensional. Equivalently, LaTeX: \{ x^1-x^0, \ldots, x^k-x^0 \} is linearly independent. For n=2, any two distinct vectors are affinely independent (k=1). Three vectors need to form a triangle; otherwise, they are co-linear and are affinely dependent.

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