Introduction

Determinate linear systems:

• Trusses;
• FEM codes;
• Finite difference codes;
• Economics;
• Design optimization;
• CAD/CAM;
• ...

For a unique solution (under all conditions):

• The number of equations must be the number of unknowns (square matrix A);

  

• The matrix must be nonsingular (the determinant |A| must be nonzero).

  

Cramer's rule is useless for anything but very small systems. The general purpose method is Gaussian elimination (LU-decomposition.)