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December 12th, 2014, 06:19 PM  #1 
Newbie Joined: Dec 2014 From: Ohio Posts: 1 Thanks: 0  Relationship between singular matrices and linear dependency?
I know that when a matrix is singular it has no inverse and its determinant is 0. How does that relate to its linear dependency? How can I tell or prove this to myself? and is it the columns or rows that are linearly dependent? Last edited by skipjack; December 12th, 2014 at 08:07 PM. 
December 12th, 2014, 08:20 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,034 Thanks: 1393 
For a simple example, consider a b c d (where a is nonzero). If the determinant is zero, ad = bc, so the second row is c/a times the first row and the second column is b/a times the first column. 

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dependency, linear, matrices, relationship, singular 
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