Gauss-Jordan Elimination Calculator
Reduce a matrix to reduced row echelon form (RREF).
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Request a ToolHow to Use the Gauss-Jordan Elimination Calculator
This tool reduces any matrix to reduced row echelon form (RREF).
- Enter your matrix. Type rows separated by semicolons and values separated by commas (e.g. "1, 2, 3; 4, 5, 6").
- View the RREF. The reduced matrix updates automatically as you type.
- Copy the result. Use the Copy button to save the RREF matrix.
About Gauss-Jordan Elimination
Gauss-Jordan elimination is an algorithm that transforms a matrix into reduced row echelon form (RREF) through a series of elementary row operations: swapping rows, multiplying a row by a non-zero scalar, and adding a multiple of one row to another. The resulting RREF matrix has leading 1s in each pivot column with zeros above and below. This method is used to solve systems of linear equations, find matrix inverses, and determine the rank of a matrix.
Frequently Asked Questions
What is reduced row echelon form (RREF)?
RREF is a matrix form where each leading entry is 1, each leading 1 is the only non-zero entry in its column, and leading 1s move to the right as you go down rows.
What is the difference between Gaussian and Gauss-Jordan elimination?
Gaussian elimination produces row echelon form (upper triangular with leading 1s). Gauss-Jordan goes further to produce reduced row echelon form, with zeros both above and below each pivot.
Can I use this to solve a system of equations?
Yes. Enter the augmented matrix (coefficients and constants) and the RREF will show the solution directly if a unique solution exists.