November 22nd, 2013, 01:26 PM  #1 
Newbie Joined: Nov 2013 Posts: 26 Thanks: 0  determinant by Laplace
Hi, I want to show : ,... the case i=k was not the problem, but how i can show that if i k, the result of the sum is 0 ? hope you can help me 
November 22nd, 2013, 01:30 PM  #2 
Newbie Joined: Nov 2013 Posts: 26 Thanks: 0  Re: determinant by Laplace
maybe i have to add some information: c are the cofactors delta is the Kronecker symbol 
November 23rd, 2013, 06:49 AM  #3 
Newbie Joined: Nov 2013 Posts: 26 Thanks: 0  Re: determinant by Laplace
no ideas???

November 23rd, 2013, 09:36 AM  #4 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: determinant by Laplace
Just an observation. The result is true for any invertible matrix A by the normal inverse process. What it says, therefore, is that when det(A) = 0, the normal process for finding an inverse results in the zero matrix when you mutiply it by A. If you've shown this for j = k, then perhaps you can use the normal inverse calculations to show it for i not = j. In other words the inverse process shows that for any matrix: Where C is the cofactor matrix. 

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determinant, laplace 
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