MATH 21 Lecture Notes - Lecture 17: Linear Independence, Coefficient Matrix, If And Only If
Document Summary
Definition: linearly independent if not linearly dependent or if every finite sequence (cid:2869)(cid:1874)(cid:2869)+(cid:2870)(cid:1874)(cid:2870)+ +(cid:3038)(cid:1874)(cid:3038)= Definition: dependence relation on (cid:4666)(cid:1874)(cid:2869) (cid:1874)(cid:3038)(cid:4667) is sequence (cid:4666)(cid:2869) (cid:3038)(cid:4667) such that. The trivial dependence relation is the one with all (cid:3036)=(cid:882). A sequence (cid:4666)(cid:1874)(cid:2869) (cid:1874)(cid:3038)(cid:4667) is linearly dependent if there exists a non-trivial dependent relation. A subset of vectors is linearly dependent if there is a sequence (cid:4666)(cid:1874)(cid:2869) (cid:1874)(cid:3038)(cid:4667) contained in which (cid:4666)(cid:1874)(cid:2869) (cid:1874)(cid:3038)(cid:4667) from is linearly independent. Sequence by placing (cid:3036)(cid:3037) before (cid:3038)(cid:2869) if (cid:1862)
