Gauss-Jordan Elimination Solver

A simple C program to solve system of linear equations using Gauss-Jordan Elimination method.

Written in 2024 by Chandan Das.

---

Purpose

This program takes an augmented matrix as input and:

• Performs Gauss-Jordan elimination to reduce it to row echelon form
• Prints the reduced matrix
• Determines the rank of coefficient and augmented matrices
• Checks consistency and provides the solution (unique / infinite / no solution)

It supports up to 10×10 matrices and uses partial pivoting for better numerical stability.

Features

• Full Gauss-Jordan elimination (not just forward elimination)
• Row swapping for zero pivots
• Floating-point precision handling with EPS
• Consistency check (unique solution, infinite solutions, or inconsistent)
• Clean menu-driven interface
• Cross-platform (Windows + Linux/macOS)

How to Compile and Run

Prerequisites

• GCC compiler (or any C compiler)

Compilation

gcc -o gauss_jordan gauss_jordan.c -lm

Run

./gauss_jordan

Usage Example

System of equations:

5x + 4y = 28
7x + 2y = 39

Input:

Enter row and col of augmented matrix (limit <=10): 2 3
Enter matrix elements:
5 4 28
7 2 39

Output:

Row reduced form:
    1.0000     0.0000     5.5556
    0.0000     1.0000     0.0556

Rank of augmented matrix: 2
Rank of coefficient matrix: 2
System is consistent.
Unique solution:
(x = 5.5556, y = 0.0556)

Limitations

• Maximum matrix size: 10×10
• Handles real numbers only (no complex numbers)
• Parametric solution for infinite cases is not fully implemented yet

Future Improvements (Planned)

• Better partial pivoting (maximum element)
• Parametric form printing for infinite solutions
• Determinant calculation for square matrice

Development Journey

This project was first written in 2024 as a basic implementation using manual row operations and goto statements (original "hustle" version). No modularity, everything is in main() function. I later rewrote it with proper Gauss-Jordan elimination, better pivoting, floating-point safety using EPS. But the original provided Parametric form printing for infinite solutions . Thus, I want to include the improved parametric solution for infinite cases.

The current version is cleaner, more reliable, and follows better C programming practices.