Tool to reduce a matrix to its echelon row form (reduced). A row reduced matrix has a number of zeros starting from the left on each line increasing line by line, up to a complete line of zeros.

Matrix Reduced Row Echelon Form - dCode

Tag(s) : Matrix

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool to reduce a matrix to its echelon row form (reduced). A row reduced matrix has a number of zeros starting from the left on each line increasing line by line, up to a complete line of zeros.

An **reduced row echelon form matrix** (RREF) is a matrix of the form $$ \begin{bmatrix} \oplus & * & * & * \\ 0 & 0 & \oplus & * \\ 0 & 0 & 0 & \oplus \\ 0 & 0 & 0 & 0 \end{bmatrix} $$

The $ * $ are any coefficients and the $ \oplus $ are non-zero coefficients called pivots.

A **row reduced matrix** is an echelon matrix whose pivots are 1 with coefficients in the column of the pivot equal to zero.

$$ \begin{bmatrix} 1 & * & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{bmatrix} $$

The transformation method of any matrix into a reduced row echelon matrix is possible by means of row operations such as:

- the permutation of 2 rows

- the multiplication of a row by a non-zero constant

- the addition of a row or a multiple of a row

Example: The matrix $$ \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 8 \\ 0 & 0 & 0 \end{bmatrix} $$ can be reduced in a matrix **echelon form** $$ \begin{bmatrix} 1 & 2 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix} $$ in two steps : 1/ Multiplication of row 2 by 1/2 (or division by 2) $ \begin{bmatrix} 2 & 4 & 8 \end{bmatrix} $ becomes $ \begin{bmatrix} 1 & 2 & 4 \end{bmatrix} $ and 2/ subtraction of row 2 to row 1 $ \begin{bmatrix} 1 & 2 & 4 \end{bmatrix} - \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 1 \end{bmatrix} $.

dCode retains ownership of the source code of the script Matrix Reduced Row Echelon Form online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Matrix Reduced Row Echelon Form script for offline use on PC, iPhone or Android, ask for price quote on contact page !

matrix,echelon,row,reduction,form,pivot,rref

Source : https://www.dcode.fr/matrix-row-echelon

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲