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June 3rd, 2014, 11:24 AM  #1 
Member Joined: Nov 2013 Posts: 47 Thanks: 4  Determinant proof for 3 by 3 matrices
To get the determinant of 3 by 3 matrices we're told to just reduce the 3 by 3 matrix into three 2 by 2s by essentially taking 3 terms in the matrix and eliminating their column and row and then multiplying those terms by their respective 2 by 2 submatrices. I'm able to use the method, but I don't like blindly applying methods like this without having at least some intuition of why they work. I've looked at a geometric proof for why the determinant of a 2 by 2 matrix is adbc and it makes sense, but I havent been able to find a proof for the method that I described above. Why in the world does that work?

June 4th, 2014, 08:18 PM  #2 
Newbie Joined: Jun 2014 From: USA Posts: 21 Thanks: 2 
It is possible by multiplication only there is not any other option to change 3 by 3 matrix in 2 by 2.


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