4x4 determinant

[jebeagles]

I was doing a math project, and I was wondering if anyone knew how to solve a 4x4 determinant.

[Jhaqen]

Convert it to it's upper triangular form using Gaussian Elimination and the determinant should be the product of it's diagonal elements. I think.

[robphy]

You could expand by minors
http://ceee.rice.edu/Books/LA/det/det2.html
http://mathworld.wolfram.com/DeterminantExpansionbyMinors.html

[MiGUi]

Aplying the permutation definition, you will have 24 terms to sum. Its much easier to do by minors.

[HallsofIvy]

The DEFINITION of a genereal n by n determinant is this: form all possible products taking one number from each row and column. There will be n! ways to do this. If you write the terms so that the numbers are in order of the columns, the row numbers will be a permutation of 1,2,3...n. Multiply each product by -1 if this is an odd permutation, 1 if even permutation, and add.

The simplest way to calculate it is row reduce as Jhageb suggested.

Second simplest way is to "expand by minors".