The first part of this spreadsheet implements the procedure discussed on page 155 of Engineering with Excel, 2nd Edition, by Ronald W. Larsen, Prentice-Hall E-Source (2005).  We solve a 3×3 system of linear equations.  First we use the Excel MINVERSE function for the inverse of a matrix. The second part uses a home-made VBA subroutine to accomplish the same thing.

For large systems of linear equations, both full and sparse, LAPACK is a much better alternative for direct solutions.   Help using Lapack’s Fortran routines within a Windows environment can be found online.