Author: Teresa Jurlewicz, Zbigniew Skoczylas. Definicje, twierdzenia, wzory; [5] Mostowski A. Jurlewiczz of Exact Sciences. The main aim of study: The whole-number operations of addition, subtraction, multiplication and division and their properties form the foundation of arithmetic.

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Groups, fields, linear spaces. Group homomorphism, field isomorphism, vector space linear transformation. Structure of linear spaces. Linear combination of vectors, span of a set of vectors.

Linear independence, basis, and dimension; linear subspace. Coordinates of a vector relative to a basis , matrix representation of a vector,. Linear transformations between finite-dimensional vector spaces. Matrix representations of linear transformations. Algebraic operations on matrices. Composition of linear transformations and matrix multiplication. Linear combination of vectors and matrix multiplication.

Algebraic and geometric structure of the field of complex numbers. Complex numbers as ordered pairs of real numbers, an extension of the real numbers by adjoining an imaginary unit, complex numbers as matrices of linear transformations in R2.

Geometric interpretation of complex numbers. Exponentiation and root extraction. Matrices and determinants. Matrix multiplication non-commutative. Matrix invertibility. Inverce matrix. Oriented volume. Vector and matrix forms of systems of linear equations.

Existence and number of solutions: the Kronecker-Capelli theorem. Solution methods for systems of linear equations. Kernel and image of a linear transformation, pre-image of a vector and related systems of linear equations. Geometric interpretation of solution sets of homogeneous and non-homogeneous systems of linear equations as linear and affine subspaces in Rn.

Equivalence relations. Relation between two sets, graph, function. Definitions, theorems, proofs. Coordinates of a vector relative to a basis , matrix representation of a vector, 6. Complex numbers as ordered pairs of real numbers, an extension of the real numbers by adjoining an imaginary unit, complex numbers as matrices of linear transformations in R2 9.

Jurlewicz, Z. Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:.

Additional information registration calendar, class conductors, localization and schedules of classes , might be available in the USOSweb system:. Organized by: Faculty of Mathematics and Natural Sciences. School of Exact Sciences. Related to study programmes: Mathematics - part-time first-cycle studies Mathematics - full-time first-cycle studies.

Cartesian products. Relations orderings, partitions and equivalence relations. You are not logged in log in.

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## Algebra liniowa 1: przykĹ‚ady i zadania

Objectives of the course: Introduction to linear algebra. Basic algebraic structures groups, fields, linear spaces and properties of algebraic operations. Applications of matrices, elementary matrix operations, determinants and vectors to the analysis of the following three, stricly connected problems:. Cartesian products. Relations orderings, partitions and equivalence relations.

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## JURLEWICZ SKOCZYLAS ALGEBRA LINIOWA 2 PRZYKADY ZADANIA PDF

Groups, fields, linear spaces. Group homomorphism, field isomorphism, vector space linear transformation. Structure of linear spaces. Linear combination of vectors, span of a set of vectors. Linear independence, basis, and dimension; linear subspace. Coordinates of a vector relative to a basis , matrix representation of a vector,. Linear transformations between finite-dimensional vector spaces.