IsRowEchelonForm

Tests if a matrix is in row echelon form.

Syntax

• IsRowEchelonForm(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

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

• all rows consisting of only zeros are at the bottom

• the pivot entry of each non-zero row is strictly to the right of the pivot pivot entry of the row above it.

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⎠

IsRowEchelonForm(A)

true

See also

• IsReducedRowEchelonForm

• PivotPos

• IsZeroRow

• RowEchelonForm