About Gaussian Elimination

Gaussian elimination is a fundamental algorithm in linear algebra for solving systems of linear equations. This calculator provides a step-by-step solution using row operations to transform the augmented matrix into row echelon form, then performs back substitution to find the solution vector.

How to Use This Calculator:

1. Select dimensions: Choose the number of equations (rows) and variables (columns)
2. Enter coefficients: Fill in the coefficient matrix and constant terms
3. Solve: Click "Solve System" to see the solution and all intermediate steps
4. Randomize: Use the randomize button to generate practice problems

Key Features:

• Step-by-step solutions: See each row operation performed
• Partial pivoting: Automatically handles zero pivot elements
• Error detection: Identifies singular and inconsistent systems
• Multiple sizes: Supports systems from 2x2 up to 5x5

Example Problem:

For a 2×2 system of equations:

Enter the augmented matrix as:

Applications of Gaussian Elimination:

• Solving systems of linear equations in engineering and physics
• Finding matrix inverses and determinants
• Computer graphics and machine learning algorithms
• Economic modeling and operations research