Courses

Matrixes. Operations with matrices and their basic properties. Scalar matrices. Matrix rank. Inverse and inverse of a matrix. Elementary matrices and elementary operations of lines. Equivalent matrices. Calculation of the inverse matrix by reduction to reduced scalar form. Determinant of a square matrix. Properties of determinants. Minor and algebraic complements. Finding the inverse matrix using determinants. Methods for solving systems of linear equations (Gauss method and Cramer method). Investigation of the system. Homogeneous systems of linear equations. Vector space of free vectors. Vector operations. Linearly dependent and linearly independent vectors. Orientation of the plane and space. Coordinate systems in the plane and in space (general, orthogonal and polar). Transformations of coordinate systems. Vector Algebra (inner, outer and mixed product, applications in the calculation of areas and volumes). Line and plane in space (parametric equations, vector equation, equations of the line as an intersection of planes, Cartesian equation of the plane). Bundle of parallel planes. Bundle of planes intersecting by a line. Distance of a point from the line and plane. Distance between lines. Orthogonal projections. Quadratic surfaces. In order to highlight the special elements of pedagogical and teaching competence contained in the course, emphasis is placed on its historical evolution, the development of its cognitive object, but also on its applications in technology and/or other sciences.