Question

Can anyone explain the reduction method used to calculate the determinant of a large square matrix?

Answer 1

It is credited to lewis carroll

Answer 2

I did not know that^
interesting...
basically all it is is using elimination to get the matrix to be upper-triangular, which makes the derivative easier to compute
here are some good notes on the topic
http://tutorial.math.lamar.edu/Classes/LinAlg/DeterminantByRowReduction.aspx

Answer 3

the determinant easier to compute*

Answer 4

Thanks turing :D That is exactly what i needed

Answer 5

happy to help!

Answer 6

http://www.maa.org/mathtourist/mathtourist_03_19_07.html

Answer 7

I think this is the one I was referring to. It is actually quite interesting

Answer 8

Oh, this is a little different that the method I linked you to.
Never seen this one before, but it seems cool.

Answer 9

yup never ever seen it either. I dont think it is used now a days

Answer 10

The link you showed me is news to me
do you want me to try to clear up anything about it in particular?

Answer 11

ummm can u just say in short what he did?

Answer 12

I have to write a lil paragraph abt it

Answer 13

only if u want to:D You dont have to

Answer 14

Turing I am not taking advantage over you:D All this while i am jotting down points

Answer 15

Well like I said this is new to me
but it looks like we started with our 4x4 matrix A, which we duplicated all the middle rows and columns of.
we then broke up the resulting 6x6 matrix into 3 2x2 matrices which we took the determinant of.
this gives us a 3x3 matrix which we did the same to:
duplicate all middle rows and columns, which gives a 4x4 matrix.
The central term -7 is duplicated in all matrices, so that factor will need to be divided out in the end.
after breaking up our 4x4 into 4 2x2 matrices (which we take the det of) we have a 2x2 which we take the det of.
remembering to divide out the extra factor of -7 we picked up earlier gives us the final det.

-Don't worry, this was interesting and new, thanks for showing me.
I hope what I noticed about the problem helped, though since I am new to the method I'm not sure I can generalize it.
Good luck!

Answer 16

Thanks Turing