Is There a Faster Way to Find the Reduced Row Echelon Form of a Matrix?

[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?

 

[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.

 

[Defennder]

Just thought about this a little longer and realized 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.

 

[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.

 

[rocomath]

Lol much quicker! )

 

[Defennder]

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