The conditions for affine dependence are stronger than those for linear dependence, so an affinely dependent set

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The conditions for affine dependence are stronger than those for linear dependence, so an affinely dependent set is automatically linearly dependent. Also, a linearly independent set cannot be affinely dependent and therefore must be affinely independent. Construct two linearly dependent indexed sets S₁ and S₂ in R₂ such that S₁ is affinely dependent and S₂ is affinely independent. In each case, the set should contain either one, two, or three nonzero points.

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Let S 1 consist of three distinct points on a line through the origin The set is affinely depend...View the full answer

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