Linear Algebra Intermediate

RREF Calculator

Enter an augmented matrix and reduce it to Reduced Row Echelon Form (RREF). Every row swap, scaling, and elimination is shown step by step so you can follow the reasoning — not just the answer.

Subject: Linear Algebra
Input: Augmented matrix
Output: RREF + solution + steps
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Enter Your Matrix
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Result
Enter matrix values and click Calculate
RREF Matrix
Solution
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Row Operation Steps
What RREF Computes
Each pivot = 1, column has zeros above & below

RREF (Reduced Row Echelon Form) transforms any augmented matrix [A | b] into a canonical form where each pivot column contains exactly one 1 and all other entries in that column are 0.

Three row operations are used: swap two rows, scale a row by a non-zero constant, and add a multiple of one row to another.

Exam tip — every system of linear equations has exactly one RREF, so two students using different row operation orders always get the same final matrix.
When To Use RREF
  • Solving a system of linear equations (unique, infinite, or no solution)
  • Finding the rank and null space of a matrix
  • Computing the matrix inverse (augment with identity)
  • Determining linear independence of a set of vectors

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