Linear equations MOC

Row echelon form

Row echelon form (REF) is a manipulated form of a system of linear equations that enables back substitution in order to find a solution. A system may be converted to this form by the process of Gaußian elimination.

A matrix is in row echelon form iff.¹

1. Any rows of the matrix consisting entirely of zeros occur as the last rows of the matrix, and
2. The first non-zero entry of each row is in a column strictly to the right of the first non-zero entry in any of the earlier rows,

A matrix in reduced row echelon form allows the identification of Basic and free variables.

Reduced row echelon form

Reduced row echelon form (RREF) is a modified version of REF which allows solutions to be read off the matrix trivially. Similarly, they may be produced by the process of Gauß-Jordan elimination.

The additional conditions for a matrix to be in RREF are

1. All leading entries are , and
2. All leading entries are the only entry in their respective column.

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