RREF Calculator

Reduce a matrix to row reduced echelon form with transparent Gauss-Jordan steps. Ideal for solving augmented systems, checking pivot structure, and learning linear algebra.

Matrix input
Enter a matrix and apply Gauss-Jordan elimination to reach row reduced echelon form.
What the calculator returns

1. The final row reduced echelon form.

2. Every swap, scaling, and elimination step used to get there.

3. The matrix rank inferred from the pivot rows.

4. A layout that works for augmented matrices used in linear systems.

Result
RREF makes pivot columns easy to spot and helps classify linear systems.

Calculate the matrix to see its reduced form and row operations.

How Gauss-Jordan elimination works

1. Pick a pivot column and move a nonzero entry into the pivot row.

2. Scale the pivot row so the pivot becomes 1.

3. Eliminate every other entry in that pivot column.

4. Repeat to the right until there are no pivot columns left.

What you can read from RREF

Pivot columns identify basic variables.
Zero rows help determine the matrix rank.
Augmented matrices show whether a system has one solution, infinitely many, or none.

Frequently asked questions

What is RREF?

RREF stands for row reduced echelon form. In this form, every pivot is 1, each pivot is the only nonzero entry in its column, and pivot positions move to the right as you go down the matrix.

Why is RREF useful?

RREF is useful for solving systems of linear equations, finding matrix rank, checking consistency, and reading solution structure directly from an augmented matrix.

What is the difference between REF and RREF?

REF only requires zeros below each pivot. RREF goes further by scaling each pivot to 1 and clearing the entries above the pivot too.

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