Can You Use the Appended Matrix Method for 4x4 Determinants?

[Kevin McHugh]

I know row reduction methods are the best way to calculate the determinant of large matrices. I was wondering if you can use the appended matrix method to calculate the determinant of a 4x4 by appending the matrix with the first 3 columns. There should be n! terms, but I only get 8 instead of 24.

 

[jfizzix]

I don't think the appended matrix method works for larger than 3x3 matrices for that reason.

The only other way I know for calculating the determinant is expansion by minors, which is n! terms, in principle, but it's a lot easier than it sounds if you have a lot of zeroes and ones.