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) : Mathematics, Algebra, Symbolic Computation

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. 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, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Matrix Reduced Row Echelon Form script for offline use, for you, your company or association, see you on contact page !

matrix,echelon,row,reduction,form,pivot

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

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode