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May 21st, 2009, 05:15 AM  #1 
Newbie Joined: May 2009 Posts: 15 Thanks: 0  Linear Algebra  Singularity problem
Hi all, I'm having a little trouble with a simple question: I have to proof that if A is singular, and B is not, then AB is singular 
May 21st, 2009, 07:20 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Linear Algebra  Singularity problem
Hint: A matrix is singular iff 
May 21st, 2009, 10:55 AM  #3 
Newbie Joined: May 2009 Posts: 15 Thanks: 0  Re: Linear Algebra  Singularity problem
Actually I'm trying to prove that det(AB) = det(A)*det(B), so I can't use this equation and, naturally, have to start by the case where A or B or both are singular... still looking for an answer, or a hint 
May 21st, 2009, 11:03 AM  #4 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Linear Algebra  Singularity problem
If is nonsingular, then there exists such that What can you then say about 
May 21st, 2009, 11:16 AM  #5 
Newbie Joined: May 2009 Posts: 15 Thanks: 0  Re: Linear Algebra  Singularity problem
hmmm then (BX) would be equal to A^(1), but wait a minute, A was not supposed to have an inverse, since its singular! mattpi, you're a genious!!!! sorry for bothering you with this trivial question. =D see you soon, probably I'll be back with more trivial questions! 

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algebra, linear, problem, singularity 
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