SOLVE is a MATLAB library which solves a linear system of equations A*x=b using Gauss elimination.
In MATLAB, of course, one can simply type "x = A\b" and get an answer, even if the matrix is ill-conditioned, singular, complex, rectangular (over-determined or under-determined).
Nonetheless, this library is useful because:
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
SOLVE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
LINPACK, a MATLAB library which solves linear systems for a variety of matrix storage schemes, real or complex arithmetic, and single or double precision. It includes a routine for computing the singular value decomposition (SVD) of a rectangular matrix. The original version of this library is by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
R8LIB, a MATLAB library which contains many utility routines using double precision real (R8) arithmetic.
You can go up one level to the MATLAB source codes.