123 123Calculator

(Reduced) Row Echelon Form Calculator

The (reduced) row echelon form calculator uses the Gauss (or Gauss-Jordan) elimination to find the solution of a system of up to three equations.

One row per line, values separated by commas or spaces.
Clear
Rank2the number of pivots
Size3×3
Pivot columns1, 2
Free columns1
Nullity1dimension of the null space
Full rank?No

Reduced row echelon form

10-1
012
000

The method

Gauss–Jordan elimination to reduced row echelon form

Rank answers most questions

The number of pivots after reduction is the rank — the dimension of the space the matrix actually reaches. Full rank means the columns are linearly independent and, for a square matrix, that an inverse exists. The nullity (columns minus rank) counts the independent directions the matrix crushes to zero.