Free to use, no account
RREF Calculator
Enter a rectangular matrix to calculate its reduced row echelon form (RREF), rank, pivot columns and elementary row-operation steps.
How do you find reduced row echelon form?
Use Gaussian elimination to create a leading 1 in each pivot column and eliminate every other value in that column. This calculator uses bounded numerical arithmetic and displays each row swap, scaling and elimination step.
Frequently asked questions
How do you find reduced row echelon form?
Use Gaussian elimination to create a leading 1 in each pivot column and eliminate every other value in that column. This calculator uses bounded numerical arithmetic and displays each row swap, scaling and elimination step.
Are my matrix values uploaded?
No. The matrix is processed in this browser and is not uploaded or saved by this tool.
What does RREF mean?
Reduced row echelon form has a leading 1 in each nonzero row, each pivot is the only nonzero value in its column, and pivot positions move to the right in lower rows.
How do I read pivot columns and rank?
The listed pivot columns contain leading 1s. The rank is the number of pivot columns, or equivalently the number of nonzero rows in the RREF.
Is the result exact?
No. This tool uses floating-point arithmetic and a selected zero tolerance. For exact rational work or ill-conditioned matrices, verify the result with an appropriate symbolic tool.