Author: Qurbonov, G‘ulomjon G‘afurovich; Otaqulova, Anora Jasurbek qizi

Annotation: This article discusses the concept of a system of linear equations, their importance as a mathematical model, and methods for solving them. In particular, the concepts of expressing the system in matrix form, the matrix of coefficients, the column of unknowns, and the column of free terms are explained. The steps performed in solving a system of linear equations based on the determinant, inverse matrix, and Gaussian method are also analyzed. The article, along with the theoretical foundations of the matrix method, also shows the possibilities of its application in solving practical problems. The cases of systems having a unique solution, having infinitely many solutions, or not having a solution are explained depending on the color of the matrix and the value of the determinant. The results of the study show that the matrix approach is important in solving a system of linear equations in an efficient and compact way.

Keywords: Gaussian method, system of linear equations, Cramer's method, matrix method, determinant.

Pages in journal: 583 - 588