Given a collection x1, x2, …, xk of vectors in ℝn, we say that the vectors form a linearly dependent set if one of them can be written as a linear combination of the others. That is, the set is linearly dependent if there is an index j in the range 1 to k such that
where the ci’s are given numbers.
Prove that a set of vectors xl, x2, …, xk is linearly dependent if there exist constants c1, c2, …, ck not all zero such that
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