Reduced Row Echelon Form (RREF) Calculator

Your details

Rows

Columns

Output form

Show values as

Interpret as augmented [A|b]

Row 1, Col 1

Row 1, Col 2

Row 1, Col 3

Row 1, Col 4

Row 1, Col 5

Row 2, Col 1

Row 2, Col 2

Row 2, Col 3

Row 2, Col 4

Row 2, Col 5

Row 3, Col 1

Row 3, Col 2

Row 3, Col 3

Row 3, Col 4

Row 3, Col 5

Row 4, Col 1

Row 4, Col 2

Row 4, Col 3

Row 4, Col 4

Row 4, Col 5

Result Matrix

[ 1 0 0 2 ] [ 0 1 0 3 ] [ 0 0 1 -1 ]

The matrix in reduced row echelon form (or row echelon form).

SolutionUnique solution: x = 2, y = 3, z = -1

Rank3 (out of 3 possible)

Row operations used11

Reduced Row Echelon Form computed.

Unique solution: x = 2, y = 3, z = -1
A unique solution means the system has exactly as many independent equations as unknowns.
Matrix rank: 3 (out of 3 possible).
11 elementary row operation(s) were applied.

Next stepTo verify, multiply your original matrix by the inverse (if square) or use back-substitution on the REF.