The Presentations Application (which I sell from my web site for $50) has a section called Student's Linear Equations. It is basically for didactic purposes or solving small cases. It allows you to manipulate 2D matrix structures with detailed operations such as individual operations on rows and columns, individual column pivots, converting to echelon form with or without upper triangular reduction. It also has display with row and column names to give context. You can manipulate via successive displays in a notebook, or in a Whiteboard window.
It also allows contravariant and covariant columns. There is also provision for displaying rows or columns as equation expressions, both as regular equations and as chemical composition equations or as chemical reactions. There is also provision for doing linear programming simplex operations.
Presentations is a quite large Application aimed toward writing literate notebooks with custom graphics, tables and dynamic presentations.
Dear comunity, I'm trying to play around with the simple matrixes in Mathematica for the first time and I have beginners question:
Does Mathematica have a function, which makes the intermediate step of Gaussian elimination to produce just eliminated upper triangular matrix? Function UpperTriangular only cuts the lower triangular places off (which is not what I need) and RowReduce makes the completely reduced echelon form of matrix. I needed the step in the middle of the RowReduce way.