The row reduced echelon form

Here, the derivation of the row reduced echelon form is given for several specific systems. Afterwards, the interpretation of the row reduced echelon form of a matrix is discussed.

Consider the set of equations (4.11) with

A solution vector

(4.9) | |||

(4.10) |

Subtracting three times the upper equation from the lower yields:

(4.11) | |||

(4.12) |

This set of equations is represented in a new matrix

(4.13) | |||

(4.14) |

represented in a matrix

(4.15) | |||

(4.16) |

is obtained. This is represented in the matrix

The matrix

**Overdetermined system**

The row reduced echolon form does not always contain the identity matrix. Suppose

(4.17) | |||

(4.18) | |||

(4.19) |

Here,

Suppose

(4.20) | |||

(4.21) |

Here,

The row reduced echelon form of

In MATLAB, `rref(C)`

obtains the row reduced echelon form of the matrix

Esteur 2010-03-22