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February 19th, 2010, 09:57 AM  #1 
Newbie Joined: Oct 2009 Posts: 20 Thanks: 0  Linearly dependent Theorem
I think I have the wrong interpretation of the following theorem: The nonzero vectors v1, v2,...,vn in a vector space V are linearly dependent if and only if one of the vectors vj (j ? 2) is a linear cominatin of the proceeding vects v1, v2,..., vj1. My interpretation in summary: a group of vectors is linearly dependent when there is a vector vj (being the second or greater vector) in a group of vectors is a combination of the previous vectors. There is a vector vj (being the second or greater vector) in a group of vectors that is a combination of the previous vectors when the group is linearly dependent. Now why does vj (j ? 2)? I would really appreciate if anybody could clear up my confusion and correct me of any errors. Thanks 
February 19th, 2010, 01:47 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,607 Thanks: 616  Re: Linearly dependent Theorem Quote:
 
February 19th, 2010, 02:18 PM  #3 
Newbie Joined: Oct 2009 Posts: 20 Thanks: 0  Re: Linearly dependent Theorem
Thank you. This clears a lot up. I really made it more complicated then it needed to be.


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