⬛ RREF Calculator
RREF Calculator
Reduced Row Echelon Form with every Gaussian elimination step shown. Supports augmented matrices for solving linear systems.
Row Reduction Calculator
Gauss-Jordan Elimination with full steps
✓ Step-by-Step✓ Augmented✓ Free⚡ Loading SymPy Engine…
Matrix A
Coefficient Matrix A
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Constants b
Quick Examples
What is RREF?
The Reduced Row Echelon Form (RREF) of a matrix is a unique form obtained by performing elementary row operations. A matrix is in RREF when:
- The leading entry (pivot) in each non-zero row is 1
- Each pivot is to the right of pivots in rows above
- All entries above and below each pivot are 0
- Zero rows are at the bottom
Why Use RREF?
RREF is used to solve systems of linear equations, find the rank of a matrix, determine linear independence, and find null spaces and column spaces.
Elementary Row Operations
- Swap: Exchange two rows → multiplies det by −1
- Scale: Multiply a row by a non-zero constant
- Replace: Add a multiple of one row to another