# Determinant of a 5x5 matrix

• Mar 22nd 2007, 09:39 PM
drhojo
Determinant of a 5x5 matrix
I'm in desperate need of knowing how to do this.
I already know how to get determinants of 3x3 and 4x4 matrices, but I just don't have a clue when it comes to 5x5, and google doesn't help, as I haven't found any real 5x5 examples yet (lots of 4x4 and 3x3, but only small tips for 5x5).

I understand this may be because of the large quantity of operations needed, but my assignment is to do this both MANUALLY and by making a program in C++, the problem is I can't program if I don't have a clue how to do it manually. So if anyone has a full step-by-step 5x5 example I would greatly appreciate it. Any example will do as long as it doesn't have more than one 0.

P.D. I apologize if my grammar is bad, my native language is spanish.
• Mar 22nd 2007, 09:49 PM
CaptainBlack
Quote:

Originally Posted by drhojo
I'm in desperate need of knowing how to do this.
I already know how to get determinants of 3x3 and 4x4 matrices, but I just don't have a clue when it comes to 5x5, and google doesn't help, as I haven't found any real 5x5 examples yet (lots of 4x4 and 3x3, but only small tips for 5x5).

I understand this may be because of the large quantity of operations needed, but my assignment is to do this both MANUALLY and by making a program in C++, the problem is I can't program if I don't have a clue how to do it manually. So if anyone has a full step-by-step 5x5 example I would greatly appreciate it. Any example will do as long as it doesn't have more than one 0.

P.D. I apologize if my grammar is bad, my native language is spanish.

The wikipedia artice on determinants gives two algorithms for computing
deterninants of arbitary degree these are shown in the attachment clipped from that article.

RonL
• Mar 23rd 2007, 12:03 PM
drhojo
I've stumbled upon that wiki article before, problem is, I'm still fairly new to determinants, so most of these explanations make no sense to me (hence why I wanted a full example).

This is what I know, however :

1-To use this method :
http://img116.imageshack.us/img116/3927/matrixgx4.png
To get the determinant of a 3x3 matrix.

2-To use the "Laplace formula" to get the determinant of a 4x4 matrix by using minors and the method above for the 3x3 matrices.

I tried applying this to a 5x5 matrix, by using Laplace's formula to get 5 4x4 matrices (minors) and then using No. 1 mentioned above to get the determinants, but I'm guessing "No. 1" works only for 3x3 matrices? Because my result was incorrect.
• Mar 23rd 2007, 12:32 PM
ThePerfectHacker
Quote:

Originally Posted by drhojo
I've stumbled upon that wiki article before, problem is, I'm still fairly new to determinants, so most of these explanations make no sense to me (hence why I wanted a full example).

This is what I know, however :

1-To use this method :
http://img116.imageshack.us/img116/3927/matrixgx4.png
To get the determinant of a 3x3 matrix.

2-To use the "Laplace formula" to get the determinant of a 4x4 matrix by using minors and the method above for the 3x3 matrices.

I tried applying this to a 5x5 matrix, by using Laplace's formula to get 5 4x4 matrices (minors) and then using No. 1 mentioned above to get the determinants, but I'm guessing "No. 1" works only for 3x3 matrices? Because my result was incorrect.

That method only works for 3x3 matrices.
It can be generalized to higher matrices but you need to consider what is positive and what is negative.
That is done through "Leibniz Method" via odd/even premuations. But it is not computationally efficient.