The basic procedure:
Here's an example of a complete row reduction.
To reduce a matrix to reduced row-echelon form:
For each non-zero row in turn, from top to bottom:
Warning: Some texts don't require the leading entries for a matrix in row-echelon form to be 1's - check your text's definition to be sure.
Sometimes it is more practical not to reduce a matrix all the way to reduced row-echelon form – simple row echelon form will do. A matrix in row-echelon form (without the "reduced") is almost in reduced row-echelon form, except that you don't require that the numbers above the leading 1's be zeroes. (The numbers below the leading ones must still be zeroes, since each leading one must be further to the right than those above it.)
Here's an example
There is an important difference between the two forms, however: any matrix can be reduced to many different row-echelon forms, but can be reduced to just one reduced row-echelon form - the reduced row-echelon form of a matrix is unique.
|How to Row Reduce a Matrix|
|Introduction||Row operations and reduced row-echelon form||Gauss-Jordan elimination||Row reduction with a computer|