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Basis And Dimension Linear Algebra Pdf Download

 
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MessagePosté le: 01/09/2016, 22:24    Sujet du message: Basis And Dimension Linear Algebra Pdf Download Répondre en citant




Basis And Dimension Linear Algebra Pdf Download > shorl.com/jifristegybepre







Basis And Dimension Linear Algebra Pdf Download


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Now....I....have....to....give....you....--....or....linearly....independent....--....I'll....often....just....say....and....write....independent....for....short.....OK....I'm..looking..for..the..dimension..of..the..column..space..of..A...It..had..to..be...A....basis....for....a....vector....space....is,....is....a,....is....a....sequence....of....vectors....--....shall....I....call....them....V1,....V2,....up....to....let....me....say....Vd....now,....I'll....stop....with....that....letters....--....that....has....two....properties.....How....many....free....variables....are....there....in....terms....of....R,....the....rank,....m....--....the....number....of....rows,....n,....the....number....of....columns?....What....do....we....get?....We....have....n....columns,....r....of....them....are....pivot....columns,....so....n-r....is....the....number....of....free....columns,....free....variables.....I'm..in..two..dimensional..space,..whatever,..I'm..in..the..plane...OK...

In...the...language...of...matrices,...which...was...under...that...board,...I...could...make...those...the...columns...of...a...matrix....And....what....do....we....call....that....number?....That....number....is....--....now....I'm....ready....for....the....last....definition....today.....Yes....What...are...the...c-s?...If...c1...of...that...plus...c2...of...that...plus...c3...of...that...gives...me...0...0...0,...then...the...c-s...are...all...--...0,...right....How...do...I...know...those...are...dependent?...How...do...I...know...that...some...combination...of...V1,...V2,...and...V3...gives...me...the...zero...vector?...I...know...because...of...that....I..don't..have..to..set..those..to..zero...The..rank..of..A,..that..rank..r,..is..the..number..of..pivot..columns..and..it's..also..--..well,..so..now..please..use..my..new..word...So..this..was..another..basis..that..I..just..invented...The..conclusion..is..there..are..some..non-zero..x-s..such..that..Ax..is..zero...

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