Matrices. Matrix operations and their basic properties. Row-echelon form of matrix. Rank of a matrix. Transpose and inverse of a square matrix. Elementary matrices and elementary row operations. Equivalent matrices. Calculation of the inverse matrix by reduction to reduced row-echelon form.
Determinant of square matrix. Properties of determinants. Minors and cofactors. Finding the inverse matrix using determinants.
Methods of solving systems of linear equations. (Gauss method and Cramer method). Study of systems of linear equations. Homogeneous systems of linear equations.
Vector space. Vector operations. Linearly dependent and linearly independent vectors. Orientation of plane and space. Coordinate systems in the plane and in space (general, orthonormal and polar). Transformations of coordinate systems. Vector Algebra (dot products, cross products and mixed products and their applications in calculating areas and volumes).
Lines and planes in space (parametric equations, vector equations, equations of straight line as the intersection of two planes, Cartesian equation of a plane). Bundle of parallel levels. Bundle of planes intersecting at a line. Distance of a point from a line and a plane. Distance between lines. Orthogonal projections.
Surfaces of second degree.

In order to highlight the special educational and didactical aspects of a course, special emphasis is given on the historical evolution and scientific development of the subject as well as on its applications in technology and/or other sciences.