In connection with the updating of the content of education, the subject of computer science for secondary schools has been supplemented with new topics, and the curriculum includes the direction of work with artificial neural networks. In this regard, according to the purpose of our research, an experiment is being conducted in a number of higher educational institutions in the direction of mastering artificial neural networks for future computer science teachers. Artificial neural networks are mathematical models based on the structure of the human nervous system and their software. The work of a biological neuron can be modeled by relatively simple mathematical methods, and the whole depth and flexibility of human thinking and other important properties of the nervous system are determined not by the complexity of neurons, but by their number and the presence of a complex communication system between them. Learning to write and run the simplest neural networks on a computer without using additional devices is one of the most important skills for which you need to be able to mathematically understand artificial neural networks. During the training of future computer science teachers, we were convinced that, when explaining the creation of artificial neural networks, demonstrating their connection with mathematics, they were more effectively trained to solve complex problems. In this article, we present a method to explain the operation of artificial neural networks using linear algebra.