[MUSIC] Hello, everyone, and welcome to the fourth lecture of the Quantitative Foundations for International Business MOOC. This week is devoted to the idea of using matrices and vectors to represent economic, financial and business problems. In real world applications, most of the mathematical models used, involve many equations. Examples abound. Dynamical systems describing weather patterns and planetary movement, require complex math equation models. Closer to home, in an example where we want to consider how inflation and interest rates are determined. A model would involve at least two, and sometimes up to ten equations, describing the evolution of microeconomic variables such as unemployment, and gross domestic product, as well as inflation and interest rates. Usually, these equations contain many endogenous variables, and describe the mechanisms through which these variables depend upon several exogenous variables. In case these equations are linear, then a branch of mathematics called linear algebra can be used to solve them. Even if the equations are non-linear, a lot can be learned from linear approximations of this system of non-linear equations. This is why these models are at the center of modern economic, econometric and financial analysis. Linear algebra, then is available to help us. The consideration and analysis of sets of linear equations is much easier if we use some key mathematical concepts such as matrices and vectors. These are the subject matter of linear algebra. Of course, linear algebra is applicable elsewhere as well. For example, in the theory of differential and difference equations, in optimizations theory, and of course, statistics and trigonometrics. So the aim this week, is to provide the basic concepts of matrices, which will constitute the key starting point for further study on matrices and practical applications. We will stress the importance of concepts such as the matrix dimension, to understand the basic calculation rules involved in the manipulation of matrices. Thank you very much. [MUSIC]