What is Gaussian Elimination?

Gaussian Elimination is a fundamental algorithm used in linear algebra to solve systems of linear equations. It is named after the German mathematician Carl Friedrich Gauss and is a method that systematically reduces a matrix to row-echelon form and then to reduced row-echelon form by applying elementary row operations.

Process of Gaussian Elimination:

The process of Gaussian Elimination involves the following steps:

1. Conversion to Row-Echelon Form: The matrix is transformed into a triangular form by eliminating elements below the main diagonal using elementary row operations.
2. Back Substitution: The system of equations is solved by back-substituting the variables starting from the last equation.

Importance of Gaussian Elimination:

Gaussian Elimination is widely used in various scientific and engineering fields to solve systems of linear equations efficiently. It is the basis for many numerical methods used in computer simulations, optimization problems, and data analysis. Additionally, Gaussian Elimination is used in solving problems related to interpolation, curve fitting, and solving consistent and inconsistent systems of equations.