Gaussian Elimination Matrix Solver

This is my most recent C++ work, the Gaussian-Elimination Matrix Solver. Because this program does some very complicated pointer tricks (treating a 2-dimensional array as a vector), it is only available in C format.

The Gaussian algorithm I used is the same method that Mr. Hornbein's teaching in Foundations at the moment (2/1/99), only a tad bit simpler. Here's how it (and most other calculators) works:

Reduce the top row so that the first number is 1. Computers have no problems with fractions; humans do.
Transform the lower rows so that their rows start with zeroes. Proceed with the second row/column until the matrix is in row-echelon form.
Performs back-substitution to extract the solution from the echelon matrix.

Download source: gauss.zip (1.2K).