Reduced Row Echelon Form (RREF) Calculator
Simplify matrices to their Reduced Row Echelon Form effortlessly. Enter your matrix and let us handle the row reduction.
Enter Your Matrix
Enter the matrix row by row, separating numbers in each row by spaces or commas, and rows by new lines.
Example: 1, 2, 3
4 5 6
7,8,9
Reduced Row Echelon Form:
Step-by-step Visualization:
Step :Swap RowsScale RowRow Operation
Swap Row and Row .
Scale Row by factor .
Replace Row with Row - ( * Row ).
What is Reduced Row Echelon Form (RREF)?
The Reduced Row Echelon Form (RREF) is a simplified form of a matrix achieved through Gaussian elimination. It's used to solve systems of linear equations, find matrix inverses, and determine the rank of a matrix. In RREF, a matrix satisfies specific conditions making it easy to interpret and use in linear algebra.
Key Features of RREF:
- Leading entry (pivot) in each row is 1.
- Pivots are the only non-zero entries in their respective columns.
- Pivots are always to the right of the pivot in the row above.
- Any rows of all zeros are at the bottom.
This calculator helps you transform any matrix into its RREF, providing a step-by-step visualization of the process. Simply input your matrix and explore the simplified form and the row operations performed.
Learn more about Reduced Row Echelon Form on Wikipedia.