Gaussian Elimination Solver

This Python script was created to address a real challenge I encountered while studying for my chemical mass balance class. I needed to solve a 4x4 matrix representing a system of equations, and I wanted to implement a solution that demonstrated each step of the Gaussian elimination process. This tool allows anyone to solve a system of linear equations through Gaussian elimination while seeing every operation and transformation applied to the augmented matrix.

Features

• Step-by-Step Output: Shows each row swap, normalization, and elimination during the forward elimination phase.
• Back Substitution: Completes the solution with a clear back-substitution process.
• Detailed Solution Output: Prints the solution in a readable format with calculation time.

Requirements

• Python 3.x
• NumPy for matrix operations (install with pip install numpy)

Usage

1. Terminal Input:
   • Run the script and input the coefficient matrix and answer vector as space-separated values.
   • The script will display each step of the Gaussian elimination, showing how the solution is derived.

How to Run

python systemsolver.py

Follow the prompts to enter your matrix values, and see the full solution with all steps laid out.

Example

Input:

• Coefficient matrix A:

  2 1 -1 2
  -3 -1 2 -11
  -2 1 2 -3
  1 2 -1 -1
  

• Answer vector b:

  8 -15 -3 4
  

The output will display each row transformation and the final solution vector for the unknowns.

Why Gaussian Elimination?

Gaussian elimination is a foundational tool in linear algebra and essential for solving linear systems, especially in chemical engineering, where mass balance problems often lead to systems of equations. This script provides a clear and educational walkthrough of the Gaussian elimination process, reinforcing understanding for users who need both the solution and the methodology.

---