What's the difference between gauss-jordan reduction and gaussian elimination?

Answer 1

In mathematics, Gaussian elimination (not to be confused with Gauss–Jordan elimination), named after Carl Friedrich Gauss, is an algorithm in linear algebra for determining the solutions of a system of linear equations, for determining the rank of a matrix, and for calculating the inverse of an invertible square matrix. Formally, the Gaussian elimination algorithm takes an arbitrary system of linear equations as input and returns its solution vector, if it exists and is unique. Equivalently, the algorithm takes an arbitrary matrix and reduces it to reduced row echelon form (also known as row canonical form). Elementary operations are used throughout the algorithm

Answer 2

In short, the Gauss-Jordan reduction transform a matrix into its reduced row echelon (RRE) form, while a Gaussian elimination transforms it to its row echelon (RE) form.

To obtain the RRE, the matrix often has to be augmented before performing any operation.

Answer 3

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