Mathematically, Gaussian elimination is an algorithm in linear algebra that can be used to solve systems of linear equations, determine the rank of matrices, and find the inverse matrix of reversible matrices. When used for a matrix, the Gaussian elimination method produces a "ladder matrix". The Gaussian elimination method can be used in computers to solve thousands of equations and unknowns. However, if there are over a million equations, this algorithm will be very time-consuming. Some extremely large systems of equations are usually solved using iterative methods. There are also some methods specifically designed to solve systems of equations with specially arranged coefficients.

Gaussian elimination method calculation method：