Matrix Invrese

[Crash]

Part of my course im doing at the moment is looking at how to determine the inverse of a matrix but i just cant seem to get it, could someone explain how this is done, not in the ways by reducing the to an identity (as i know how to do this) but the proper way where a colomn and a row are deleted.......and something could someone explain this in lamens to me pls?

 

Heres a Matrix to use as an example C=(1 5 3,4 4 3,2 1 1)

[Dave]

I think you're thinking of a method used to calculate the deteminant of a matrix. Inverses of matrices are done fairly easily by row reduction. Determinants are just as easy with the method you describe - I can go into it if you want.

[Crash]

yes please that would be much appreciated

[Crash]

Is the inverse of a matrix just one over the determinant times the transpose of the matrix?

[Dapthar]

Is the inverse of a matrix just one over the determinant times the transpose of the matrix?

Nope.

 

Here's a nice introduction to matrix inversion methods. Link:

http://home.earthlink.net/~jimlux/radio/math/matinv.htm

[Crash]

Ok so i got the inverse down real good now thanks, but i dont quite know what is meant by finding the solutions of a homogenous equation (find the null vectors)

 

is that when i put the identity next to it then work through and find a matrix that will give general solution or is that when you solve for Ax=0 and then find the non trivial solutions?

[Dapthar]

Ok so i got the inverse down real good now thanks' date=' but i dont quite know what is meant by finding the solutions of a homogenous equation (find the null vectors)

 

is that when i put the identity next to it then work through and find a matrix that will give general solution or is that when you solve for Ax=0 and then find the non trivial solutions?[/quote']It's the [math]Ax = 0[/math] one.

[Crash]

So i put the matrix = to 0 and then just solve for the variables?

[Dapthar]

So i put the matrix = to 0 and then just solve for the variables?

Yup. The nontrivial solutions are primarily what one's interested in.

[Crash]

Im just working through and i did not get a trivial solution (ie no x=0) does that mean im doing it wrong?

 

Ive got

A=(3 4 7: 0

1 0 2 : 0

1 4 3 : 0)

I reduced that to

 

=(3 4 7 : 0

0 -12 -19 : 0

0 0 -5 1/3: 0)

 

that cant be right can it?

 

Do i continue to reduced row echelon form and i will get the trivial solution am i on the right track?