Linear Algebra, GA=rref(A)

1. Sep 11, 2008

rocomath

So I found the elimination matrices such that $$G_3G_2G_1A=rref(A)$$ which, but it took way too long. Is there a shorter method?

2. Sep 11, 2008

Defennder

I don't understand what were you trying to find. You want to find the matrix E such that EA = reduced row-echelon form of A ?

If so, I don't see any easy way to get it. Note that the elementary matrix corresponding to a row operation is simply the identity matrix with that same row operation performed on it. Just keep a simple record of all the types of row reduction you did, then you can easily get E from them.

3. Sep 11, 2008

Defennder

Just thought about this a little longer and realised that if all you want is the final matrix G which is a matrix product of all the E's, then one way you could get it would be to juxtapose the identity matrix next to A and and row reduce A to it's reduced row echelon form. The resultant matrix next to rref(A) would be G. If you want the composite E's you'll have to solve as above.

4. Sep 11, 2008

rocomath

That's what my classmate told me as well, I haven't verified that method yet.

I did what you said in the first post, took me forever to get G through all the E's, LOL.

5. Sep 11, 2008

rocomath

Lol much quicker!!! )

6. Sep 11, 2008

Defennder

Well the quickest way of course would be to use MATLAB. But that's cheating.