Xətti cəbrTopics

In the topic, the concept of determinant and its relationship with the matrix is ​​studied. rules for calculating two- and three-order determinants by different methods are explained. the basic properties of determinants and their application in simplifying calculations are also investigated.

In the topic, the concept of matrix, the size of the matrix and the main types are studied. the rules for addition, subtraction, number and multiplication of matrices are explained. also, matrix transposition and basic properties of transposed matrix are investigated.

In the topic, the concepts of minors and algebraic complements of matrix elements are studied. the procedure for dividing the determinant by the selected row or column is explained. also, the calculation of higher-order determinants using this method is investigated.

The subject studies the calculation of minors and algebraic complements of matrix elements. laplace's theorem explains the expansion of determinants by row or column. also, the concept of inverse matrix, its existence condition and calculation methods are investigated.

In the topic, the concept of matrix color and its main features are studied. the rules for calculating color using the method of minors and elementary transformations are explained. also, color determination using stepwise matrix form is investigated.

Concepts of linear dependence and non-linear dependence of rows and columns of the matrix are studied in the topic. the relationship between the linear dependence and the rank of the matrix is ​​explained. also, the theorem on the basis minor and its application in the study of matrices are considered.

In the subject, the writing of the system of linear algebraic equations in the form of a matrix and the basic concepts are studied. solving systems by the inverse matrix method and kramer's rule is explained. also, methods of constructing and solving matrix equations are investigated.

In the subject, the writing of the system of linear algebraic equations in the form of an expanded matrix is ​​studied. it is explained how to transform a matrix into stepwise form by means of elementary row transformations. also, the determination of cases where the system is unique, infinite or unsolvable is investigated.

The structure of the system of linear homogeneous equations and the main features of its solutions are studied in the subject. the existence conditions of non-trivial solutions of the system are explained in relation to the rank of the matrix. also, the construction of the system of fundamental solutions and the expression of the general solution are investigated.

In the subject, the concept of vector, the expression of vectors with coordinates and their main types are studied. vector addition, subtraction, multiplication, scalar, vector and mixed product operations are explained. collinearity, coplanarity of vectors and calculation of angles are also investigated.

The concept of linear space, its elements and main axioms are studied in the subject. concepts of linear subspace, linear combination of vectors, linear dependence and linear independence are explained. also, the coordinates of the base, measure, and vector on the base are examined.

Concepts of linear transformation and linear operator, their main properties are studied in the topic. the matrix expression, kernel and image of linear transformation are explained. also, the construction of the matrices of the linear operator in different bases is investigated.

In the subject, the concept of polynomial, its degree, coefficients and main types are studied. addition, subtraction, multiplication, and division operations on polynomials are explained. also, roots of polynomials, bezoun's theorem and factorization methods are examined.

In the topic, the concepts of eigenvalue and eigenvector of linear transformation are studied. it is explained how to find the eigenvalues ​​through the characteristic equation, and the eigenvectors through the corresponding system of homogeneous equations. the role of eigenvalues ​​and vectors in the study of linear transformation is also considered.

In the subject, the concept of quadratic form and its expression through a symmetric matrix is ​​studied. methods of converting quadratic form to canonical form by suitable linear transformation of variables are explained. also, the determination of the color of the quadratic shape and its main features are investigated.

In the topic, the concept of orthogonal matrix, its main properties and its relationship with the inverse matrix are studied. it is explained that orthogonal transformations preserve the length of vectors and the angle between them. the main criteria of positive definiteness of quadratic forms are also investigated.