LINEAR ALGEBRA AND ITS APPLICATIONS

Abstract. This article examines the basic concepts of linear algebra: matrices, determinants, vectors, and linear transformations. It is emphasized that matrices are an important tool for representing and solving systems of linear equations, while determinants are important for determining the existence of a solution for the system and for applying Cramer's rule. The properties of vectors (addition, scalar and vector products), linear transformations (rotation, reflection, scalar multiplication), and their practical significance are discussed in detail. The article provides examples of the application of linear algebra theory in fields such as physics (forces and moments), engineering (electrical circuits, robotics, coordinate transformations), electronics, and economics (regression, optimization). The conclusion emphasizes that linear algebra is a fundamental tool in modern science and technology, enhancing efficiency in modeling and solving complex systems. The article provides a theoretical foundation and practical guidance for students in the biomedical engineering field.

Keywords: Linear algebra, matrices and matrix operations, determinants and Cramér's rule, vectors and vector operations, linear transformations (rotation, reflection, scalar multiplication), systems of linear equations, matrix inversion, practical applications (physics, engineering, robotics, economics), biomedical engineering.