INTERPRETATION OF THE PROCESS OF MASTERING "THEORETICAL AND TECHNOLOGICAL BASES OF SOLVING THE SYSTEM OF LINEAR ALGEBRAIC EQUATIONS" IN THE TEACHING OF "ALGEBRA"

In the article, it is emphasized that systems with an arbitrary number of equations and an arbitrary number of unknowns are studied in “Algebra”, which has a special place among the compulsory subjects of the “Mathematics teaching” specialty in pedagogically oriented higher schools, and attention is directed to the possible forms of the System of Linear Algebraic Equations (SLAE). The concepts of “equivalence” and “elementary transformation” are explained by noting the important role of the concept of equivalence and equivalence of the system of equations in the study of the system of equations. Here, the complete study of a system of linear algebraic equations is “determining whether the given system has a solution, i.e. first, whether it is a joint system”, “determining whether it has a unique or multiple solutions”, “if the system is joint, finding all its solutions”, it is shown that it contains ingredients such as. Also comments on the role of the Gauss method, Kramer's rule, Kronecker-Capelli criterion, advantages and disadvantages in studying and mastering the solution of SLAE are given. The article shows that a special “categorical apparatus” conditions the process of studying the SLAE. At what level the student has mastered the essence and functions of the concepts included in these mentioned forms of spiritual education – “enabling features”, he becomes the subject of solving skills of SLAE in an adequate way.