IsReducedRowEchelonForm

Tests if a matrix is in reduced row echelon form.

Syntax

• IsReducedRowEchelonForm(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

If A is a matrix, then IsReducedRowEchelonForm(A, ε) returns true iff A is in reduced row echelon form:

• it is in row echelon form

• every pivot element is 1

• every column containing a pivot element has only zeros above and below the pivot element.

Examples

A ≔ ❨❨5, 1, 2, 3, 4❩, ❨0, 0, 2, 1, 2❩, ❨0, 0, 0, 5, 1❩, ❨0, 0, 0, 0, 0❩❩

⎛5  1  2  3  4⎞
⎜0  0  2  1  2⎟
⎜0  0  0  5  1⎟
⎝0  0  0  0  0⎠

IsReducedRowEchelonForm(A)

false

A ≔ ❨❨1, 5, 0, 0, 4❩, ❨0, 0, 1, 0, 2❩, ❨0, 0, 0, 1, 1❩, ❨0, 0, 0, 0, 0❩❩

⎛1  5  0  0  4⎞
⎜0  0  1  0  2⎟
⎜0  0  0  1  1⎟
⎝0  0  0  0  0⎠

IsReducedRowEchelonForm(A)

true

See also

• IsRowEchelonForm

• PivotPos

• IsZeroRow

• ReducedRowEchelonForm