Yesterday I saw a presentation by Cleve Moler, of MathWorks, that used M****b to create a visual transformation of a square matrix to its LU decompostion (along with permuation vector from the partial pivoting). It showed each step of the process, one by one.

Are there similar visualizations, done with Mathematica, for:

(1) Step-by-step transfromation of any given (possibly non-square) matrix to its reduced echelon form?

(2) Step-by-step transormation of any given square matrix into its LU decomposition?

By "visualization" here I do not refer to any geometric realization, just highlighting at each step the entry or entries involved and the row or rows involved and then showing the changed matrix after that step.

Moler's visualization was done, of course, with M****b, but he created it by producing scores of individual snapshots of the matrix appearance at each step and then by showing those snapshots as a discrete-time animation in Power Point.

With Mathematica, such visualization should e much easier to present, using Manipulate or, if necessary, Dynamic directly.

I don't want to "reinvent the wheel," hence this quetion.