Gaussian Elimination Calculator
Solve a system of linear equations using Gaussian elimination with back-substitution.
Enter augmented matrix [A|b]: rows by semicolons, values by commas. Last value in each row is the constant. Example: 2,1,-1,8;-3,-1,2,-11;-2,1,2,-3
How It Works
Enter the augmented matrix [A|b] where the last column is the constants. Gaussian elimination transforms the matrix to row echelon form using elementary row operations, then solves by back-substitution.
Formula
Reduce [A|b] to upper triangular form, then back-substitute
Frequently Asked Questions
What is Gaussian elimination?
Gaussian elimination is a method for solving linear systems by performing row operations to reduce the augmented matrix [A|b] to upper triangular form, then using back-substitution.
Does it work for any size system?
Yes, Gaussian elimination works for any m x n system, though this calculator handles up to 4x4 for practical use.