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November 22nd, 2013, 01:26 PM   #1
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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
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November 22nd, 2013, 01:30 PM   #2
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Re: determinant by Laplace

maybe i have to add some information:

c are the cofactors
delta is the Kronecker symbol
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November 23rd, 2013, 06:49 AM   #3
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Re: determinant by Laplace

no ideas???
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November 23rd, 2013, 09:36 AM   #4
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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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