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Linear Independence of Vectors

When a set of vectors admits no nontrivial linear relation, how to test independence for a pair (neither is a scalar multiple of the other), and why independence is what guarantees a set of coordinates is non-degenerate rather than redundant.

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Determining Linear Independence of Vectors in Linear Algebra

A set of vectors is linearly independent if and only if no vector in the set can be written as a linear combination of the others, equivalently if the only solution to the homogeneous equation k1*v1 …