Xətti cəbrSyllabus

Subject code

İF-40166y

Credits

4

Student workload

120

Semester

Autumn semester

Academic year

2025-2026

Subject type

Mandatory

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 30 saat - mühzirə b) 15 saat - seminar

Out-of-class hours

a) 45 saat - sərbəst işlər b) 30 saat - hazırlıq

Xətti cəbr fənni matrislər və determinantlar üzərində əməliyyatları, xətti fəza və bazis anlayışlarını, xətti tənliklər sisteminin həll üsullarını, evklid fəzası, ortoqonallaşdırma, xətti çevirmələr və kvadratik formaları əhatə edir. fənn tələbələrdə xətti cəbr metodlarını mənimsəmək və onları riyazi, mühəndislik və kompüter elmləri məsələlərinin həllində tətbiq etmək bacarıqlarını formalaşdırır.

• lecture
• interactive discussion
• seminar
• presentations

1. 1

   CLO 1: Performing operations on polynomials and matrices, properties and calculation rules of the determinant, laplace's theorem should be applied.

2. 2

   CLO 2: Must acquire knowledge about linear space and its basis.

3. 3

   CLO 3: He should know the system of linear algebraic equations and their solution methods, the kronecker-capelli theorem.

4. 4

   CLO 4: Must have knowledge of euclidean space and orthogonalization method.

5. 5

   CLO 5: Must acquire knowledge of linear and exponential transformations.

6. 6

   CLO 6: Must have knowledge of quadratic forms and their classification.

1. 1.
   Determinants. calculation of two- and three-order determinants. basic properties of determinants.Lecture

   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.

   • He should know how to perform operations on polynomials and matrices, the properties and calculation rules of the determinant, and the application of laplace's theorem.
2. 2.
   Matrix concept. types of matrices. operations on a matrix. transposing matrices.Lecture

   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.

   • He should know how to perform operations on polynomials and matrices, the properties and calculation rules of the determinant, and the application of laplace's theorem.
3. 3.
   Minor and algebraic complements. separation of the determinant by rows (columns). calculation of higher order determinants.Lecture

   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.

   • He should know how to perform operations on polynomials and matrices, the properties and calculation rules of the determinant, and the application of laplace's theorem.
4. 4.
   Minor and algebraic complements. calculating determinants using laplace's theorem. inverse matrix and its existence.Lecture

   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.

5. 5.
   The rank of the matrix. calculation of color by different methodsLecture

   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.

   • He should know how to perform operations on polynomials and matrices, the properties and calculation rules of the determinant, and the application of laplace's theorem.
6. 6.
   Matrices whose rows (columns) are linearly dependent and linearly independent. theorem about the base minor.Lecture

   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.

   • Must acquire knowledge about linear space and its basis.
   • Must acquire knowledge about linear space and its basis.
7. 7.
   Xcts and its matrix form, solution by matrix method. matrix equations. kramer's ruleLecture

   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.

8. 8.
   Gaussian methodLecture

   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.

9. 9.
   System of linear homogeneous equations. a system of fundamental solutionsLecture

   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.

10. 10.
    Algebra of vectorsLecture

    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.

11. 11.
    Linear spacesLecture

    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.

12. 12.
    Linear transformation and linear operator.Lecture

    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.

13. 13.
    Algebra of polynomialsLecture

    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.

14. 14.
    Eigenvalue and eigenvector of linear transformation.Lecture

    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.

15. 15.
    Quadratic form, its representation in matrix form. bringing the quadratic form to the canonical form. the color of the square shape.Lecture

    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.

16. 16.
    Orthogonal matrix. orthogonal transformation. conditions of positive definitenessLecture

    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.

No reading list has been added.