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...Linear independence and dependence denition the set of k vectors u in rn is said to be linearly dependent if one or more can written as a combination other called independent it not aset consisting single vector i zero words there exist scalars c with at least such that this equation dependency they are only satisfy all example because thatis wewereabletoformadependencyequationinwhichatleastonethetheconstantswasn t tips for determining let then n proportional scalar multiples det matrix formed columns steps l d determine step apply don create whose solve system ux where x most easily done by row reducing augmented on right augmentation has trivial solution case every column pivot innitely many non solutions will no theorem given number same elements determinant from span important note do we line plane looking indepen dent pivots reduced form r so up nd wecan see know these three their must continue clearly innite conclude thing though two above notes...