[aseperatepeace]

How do you find the determinant of this four by four matrices by using ellimination?

MY MATRICES:

0 -2 3 -4
-5 -6 7 -8
9 -10 11 -12
13 -14 -15 16

P.S I know how to find the determinant of a three by three and a two by two easily using ellimination, but struggle with a four by four.

THANK YOU FOR YOUR TIME!

[galactus]

It is tedious to do these things by hand. In my opinion, it has become rather anachronistic to do these manually when calculators will do them lickety-split. The important thing is knowing when to use a det. Let a calculator do the grunt work. One can use cofactors. Or, using row reduction methods, turn the matrix into a upper or lower triangular matrix and bring out common factors to multiply.

I will tell you the determinant is -2128.

There is something to shoot for if you want to give it a go.

There are some det laws that are helpful to know.

Here is an example of what I mean.



Interchange first and second rows:



Remove a common factor of 3 from the first row:



-2 times first row added to third row:



-10 times second row added to third row:



Remove a common factor of -55 from the last row: