Tool to reduce a matrix to its echelon row form. 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, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

Tool to reduce a matrix to its echelon row form. 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 **echelon form matrix** 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 of any matrix into a reduced row echelon matrix is possible by means of operations such as the permutation of 2 lines, the multiplication of a line by a non-zero constant or the addition of a line or a multiple of a line.

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 given for free. So if you need to download the online Matrix Reduced Row Echelon Form script for offline use, check contact page !

matrix,echelon,row,reduction,form,pivot

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

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback