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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 k values are 0. | 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 k values are 0. | ||
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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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| + | [[Linear_Algebra_Resource|Back to Linear Algebra Resource]] | ||
| + | [[MA351|Back to MA351]] | ||
[[Category:MA351]] | [[Category:MA351]] | ||
Revision as of 04:54, 18 August 2010
When are vectors linearly independent?
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.
