Step by Step solution about How to resolve the algorithm Reduced row echelon form step by step in the Mathematica/Wolfram Language programming language

The given Wolfram code performs the operation of row reduction on a matrix. Row reduction is a mathematical technique used to transform a matrix into an equivalent matrix in row echelon form or reduced row echelon form. It involves applying elementary row operations, such as swapping rows, multiplying rows by a constant, and adding multiples of one row to another row.

Here's a detailed explanation of each part of the code:

RowReduce: This is a built-in function in Wolfram Language that performs row reduction on a matrix. It takes a matrix as input and returns a reduced row echelon form of the matrix.

{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}} : This is the input matrix. It is a 3x4 matrix with three rows and four columns.

RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}] : This line applies the RowReduce function to the input matrix. It performs row operations to transform the matrix into reduced row echelon form.

The output of the code will be the reduced row echelon form of the input matrix. The reduced row echelon form is a matrix in which each row has a leading 1 (the first non-zero element from left to right), and the leading 1s occur in different columns. All other elements in the columns with leading 1s are 0.

By performing row reduction, you can solve systems of linear equations, find the rank and null space of a matrix, and perform other matrix operations more efficiently.

RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]