Gaussian Elimination for Linear Systems

Overview

This Python project provides functions for solving linear systems of equations using the Gaussian elimination method. The implementation includes functions for obtaining coefficients, calculating determinants, performing Gaussian elimination, back-substitution, and displaying solutions.

Functions

1. get_coeffs

Prompt the user to enter the number of unknowns and populate a matrix with coefficients for a linear system.

2. calculate_determinant

Calculate the determinant of a square matrix using NumPy's np.linalg.det function.

3. gaussian_elimination

Perform Gaussian elimination on an augmented matrix to transform it into upper triangular form.

4. back_substitution

Solve a linear system in upper triangular form using back-substitution.

5. triangularization

Combine Gaussian elimination and back-substitution for efficient solution finding.

6. display_solution

Print the solution vector in a readable format.

7. solve_linear_system

Main entry point: obtain coefficients, calculate determinant, and solve the linear system using Gaussian elimination.

Usage

1. Clone the repository:

   git clone https://github.com/Kaoutherbo/Gaussian_Elimination-Method.git

2. Navigate to the project directory:

   cd Gaussian-Elimination-Method

3. Run the main script:

   python main.py

Follow the on-screen instructions to input coefficients and obtain solutions.

Dependencies

• NumPy: Installation instructions

Contributing

If you would like to contribute to this project, please follow the guidelines in CONTRIBUTING.md.

License

This project is licensed under the MIT License.