(New page: A (finite) set of vectors <math>v_1, v_2...v_m</math>is said to be linearly independent if and only if the equality <math>k_1v_1+k_2v_2+...k_mv_m=0</math> is true exactly when all the ...) |
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If a set of vectors are not linearly independent, then they are linearly dependent. | If a set of vectors are not linearly independent, then they are linearly dependent. | ||
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Revision as of 13:18, 18 January 2009
A (finite) set of vectors $ v_1, v_2...v_m $is said to be linearly independent if and only if the equality $ k_1v_1+k_2v_2+...k_mv_m=0 $ is true exactly when all the k values are 0.
This is equivalent to saying you can't come up with any linear combination of $ v_1 $ and $ v_2 $ that equals v_3, or $ v_1...v_3 $ that equals $ v_4 $... or $ v_1...v_{m-1} $ that equals $ v_m $.
If a set of vectors are not linearly independent, then they are linearly dependent.
