I have a square matrix A. I want to row reduce it so it is in Upper Triangular form. When row reducing you perform operations which can also be represented with matrices that are just multiplied to the matrix A. I want to supply the matrix A and have returned the reduced matrix E and the matrix which represents all of the row operations R such that RA=E.
I can do this by hand, and spent too much time on a 9x9 matrix, but I would like to check my work. I just don't know what this is called. I'm not decomposing the matrix and RowReducing just returns the completed matrix.