Linear algebra is used in many mathematical disciplines and in natural and social sciences. In this thesis we want to show some applications of linear algebra in economics and game theory. Input-output analysis is of great importance in economics. It is based on assumption that the production system of the economy can be divided into certain number of interrelated production sectors. Each sector in a production of its products uses products of other sectors or even of its own sector. Besides giving the products to other sectors, each sector gives its products to final consumers. Therefore, the total level of production of a particular sector depends on the requirements of other production sectors and final consumers for its products. The interdependence between sectors is shown in input-output table. The question is what level of production each of the sectors must have in order to meet the total demand for their products. The answer is given by Leontief’s input-output model. In the past period, three basic versions of the input-output model have been developed: the open static model, the closed static model, and the dynamic model. In this thesis, the focus is on the open static input-output model. Besides explaining the method of input-output analysis, in the first chapter we have briefly described the historical development of the analysis. The author who contributed the most to its development is Wassily Leontief. In the second chapter, we have presented Leontief’s open input-output model and have given the assumptions which model must satisfy. The model is based on solving a system of n linear equations with n unknowns, so linear algebra and knowledge of matrices play an important role here. We have proved theorems that guarantee the existence and uniqueness of a non-negative model solution and the existence of an economically meaningful solution under certain conditions. At the end of the chapter, we have given the example of Leontief’s open input-output model. In the third chapter, we have shown the applications of linear algebra in game theory. The focus is on matrix games and before the examples of matrix games, we have defined the fundamental concepts on which game theory is based.