⬛ 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