1. ## matrix

can someone tell me how you take the determinant of a 4X4 and 5X5 matrix

l a1 a2 a3 a4 a5 l
l b1 b2 b3 b4 b5 l
l c1 c2 c3 c4 c5 l
l d1 d2 d3 d4 d5 l
l e1 e2 e3 e4 e5 l

and

l a1 a2 a3 a4 l
l b1 b2 b3 b4 l
l c1 c2 c3 c4 l
l d1 d2 d3 d4 l

dan

3. I never used cofactors to find determinants of 3 by 3 matrices.

If I extended my method to 4 by 4 I would get for the matrix:

a b c d
e f g h
i. j. k l
m n o p

(afkp + bglm + chin + dejo) - (dgjm + cfip + belo + ahkn)

Is this correct? If so would I be able to extend it for any square matrix

4. Originally Posted by Glaysher
I never used cofactors to find determinants of 3 by 3 matrices.

If I extended my method to 4 by 4 I would get for the matrix:

a b c d
e f g h
i. j. k l
m n o p

(afkp + bglm + chin + dejo) - (dgjm + cfip + belo + ahkn)

Is this correct? If so would I be able to extend it for any square matrix
Sadly, I think that method only works for 3x3

5. Originally Posted by ThePerfectHacker
Sadly, I think that method only works for 3x3
i know that that's true...

6. Originally Posted by Glaysher
I never used cofactors to find determinants of 3 by 3 matrices.

If I extended my method to 4 by 4 I would get for the matrix:

a b c d
e f g h
i. j. k l
m n o p

(afkp + bglm + chin + dejo) - (dgjm + cfip + belo + ahkn)

Is this correct? If so would I be able to extend it for any square matrix
Is this not a particular case of Leibniz's formula (see here) ?

RonL

7. Originally Posted by CaptainBlack
Is this not a particular case of Leibniz's formula (see here) ?

RonL
But that is not necessary the ideal method. Because then you need to compute whether the premutations are even or odd--> That is time consuming.

8. Originally Posted by CaptainBlack
Is this not a particular case of Leibniz's formula (see here) ?

RonL
you tell me ... I did'nt get half of that explnation...
dan

9. Originally Posted by dan
you tell me ... I did'nt get half of that explnation...
dan
Yes it is

RonL

10. Originally Posted by ThePerfectHacker
But that is not necessary the ideal method. Because then you need to compute whether the premutations are even or odd--> That is time consuming.
Now if I recall I never said it was the ideal method of computing it.

happens for cubics and quartics, just because I might mention the
existence of the corresponding formulae does not mean that I recommend
their use for anything other that as a decorative element for a wall
paper design

RonL

(Oh and it/they may have some use as the machinery in the proof
of other results)

11. I'm amazed I still remember anything about permutations. So much of the stuff I did at uni has been lost to the void. The formula looks familiar enough for me to think I've seen it before. It would have taken ages to find it though and I hadn't even thought to look. Thanks for satisfying my curiousity.