I'm writing functions for my matrix class that will find the inverse of a matrix and will put a system in row reduced echelon form.
I have a pretty good idea of how I'll manage with forward elimination - create an elimination matrix, like so:
|1 0 0|
|-2 1 0|
|0 0 1|
and multiply it by the matrix, which would subtract twice the first row from the second row.
BUT to do rref or to find an inverse, I must be able to do BACKWARDS elimination - I understand the concept perfectly on paper, but I would like to be able to put it in terms of an elimination matrix for my program. i.e, what elimination matrix would you need to change (1,2) in the following matrix into a 0:
|2 2 0|
|0 3 0|
|0 0 5|
Or is there no elimination matrix that does this (perhaps thats why our teacher didn't say what it was) and I must just write a function to do the actual multiplying of a row and subtracting it from another row?