heure_81 - Ind ependance lin eaire et syst` eme libre...

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Unformatted text preview: Ind ependance lin eaire et syst` eme libre Rappel { vector i , vector j } est un syst` eme g en erateur de V 2 . { vector i , vector j , vector k } est un syst` eme g en erateur de V 3 . Tout vecteur de V 2 ou V 3 se d ecompose de fa con unique selon ces syst` emes. Ind ependance lin eaire et syst` eme libre D efinition Soient p vecteurs vector v 1 , vector v 2 , ..., vector v p de V . { vector v 1 , vector v 2 , ..., vector v p } est dit libre ou lin eairement ind ependant si aucun des vector v i nest combinaison lin eaire des vecteurs { vector v 1 , ..., vector v i- 1 , vector v i +1 , ..., vector v p } , i.e. si aucun des vector v i ` a lespace engendr e par les autres vecteurs. Un syst` eme qui nest pas libre est dit li e ou lin eairement d ependant . Ind ependance lin eaire et syst` eme libre Exemple Soient vector v 1 = 3 vector i + vector k , vector v 2 = 5 vector j 2 vector k et vector v 3 = 12 vector i 5 vector j + 6 vector k . { vector v 1 , vector v 2 , vector v 3 } est un syst. g en. li e car vector v 3 = 4 vector v 1 vector v 2 . { vector v 1 , vector v 2 } est un syst. g en. lin. ind ep. Ind ependance lin eaire et syst` eme libre D efinition Soient p vecteurs vector v 1 , vector v 2 , ..., vector v p de V . Un ens. ou un syst. de vecteurs vector v 1 , vector v 2 , ..., vector v p est libre ou lin eairement ind ependant si l equation a 1 vector v 1 + a...
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This note was uploaded on 11/07/2010 for the course CIV 3930 taught by Professor Montes during the Spring '10 term at École Polytechnique de Montréal.

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heure_81 - Ind ependance lin eaire et syst` eme libre...

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