Gaussian Elimination Solver
Step-by-step solver for systems of linear equations using Gaussian elimination.
Enter Augmented Matrix
| x | Constants |
|---|---|
Solution
Step-by-step Solution
Swap Row and Row .
Perform row operation: Row = Row + () * Row .
About Gaussian Elimination
Gaussian Elimination is a method used in linear algebra to solve systems of linear equations. It systematically transforms a system of equations into an equivalent upper triangular form (row echelon form) which can then be easily solved using back substitution.
- Augmented Matrix: The system of equations is represented as an augmented matrix, combining the coefficients and constants.
- Elementary Row Operations: The method involves performing elementary row operations such as swapping rows, multiplying a row by a non-zero scalar, and adding a multiple of one row to another to simplify the matrix.
- Row Echelon Form: The goal is to transform the matrix into row echelon form, making it easier to find the solution.
- Applications: Gaussian elimination is fundamental in various fields like engineering, computer science, and economics for solving linear systems and matrix computations.
This tool helps you solve systems of linear equations by entering the augmented matrix and viewing the step-by-step process of Gaussian elimination. For further reading, you can refer to resources on linear algebra and numerical methods.