I seem to be still having problems with solving the determinant of a 4x4 matrix correctly. There are two methods I can use: Factor/Cofactor and reduction to triangular form.(adsbygoogle = window.adsbygoogle || []).push({});

Ex:

[ 1 2 3 4

-5 2 1 0

6 4 3 2

1 1 1 1]

determinant is 2 based on the calculator

Factor/Cofactor: I did:

1*det[2,1,0; 4,3,2; 1,1,1] - 2*det(-5,1,0;6,3,2; 1,1,1]

+ 3*det[-5,2,0; 6,4,2; 1,1,1] -4*det(-5,2,1; 6,4,3; 1,1,1]

From there I would do the individual det of the 3x3s, but when everything is added up I'm getting a determinant of 0! Did I set things up correctly like on the process of setting up the factor/cofactor method.

With the reduction to triangular form, it looks similar to Guassian elimination where I'm trying to get the matrix reduced to upper triangular form. I know that each row swap I make I need to multiply by (-1). When I'm done I mulitply the terms outside the matrix to the diagonals. However, I'm still a bit confused, so can anyone explain it a bit better than my textbook?

Thanks.

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# 4x4 Matrix

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