Reduced row echelon form

From Wikipedia, the free encyclopedia

In mathematics, a matrix is in reduced row echelon form (also known as row canonical form) if it satisfies the following requirements:

• All nonzero rows are above any rows of all zeroes.
• The leading coefficient of a row is always to the right of the leading coefficient of the row above it.
• All leading coefficients are 1.
• All entries above a leading coefficient in the same column are zero.

It is readily seen that these conditions are stronger than those for row echelon form. Therefore, every matrix in reduced row echelon form is in row echelon form.

Unlike row echelon form, every matrix reduces to a unique matrix in reduced row echelon form by elementary row operations. (See Elementary matrix transformations.)

[edit] Examples

The following matrix is in reduced row echelon form:

However, the following matrix is not in reduced row echelon form, as the leading 1 in the third row is not the only nonzero entry in its column:

[edit] See also

• Gaussian elimination
• Gauss–Jordan elimination
• Row echelon form

[edit] External links

• Calculate the reduced row echelon form online