[MUSIC] The material presented in quantitative foundation for international business has dealt, up to this point, with mathematical models having a relatively low number of variables and functions. However, most of the mathematical models used by economists and business analysts ultimately involve many equations and variables. In turn, they usually express one or more of the endogenous variables as depending on several exogenous variables and parameters, and using many functions. Put another way, they use a system of equations, the most famous of which is probably the supply and demand system. These equations may or may not be linear. In case all of the equations in such systems are linear, then the material belongs to an area of mathematics called linear algebra. Linear algebra is very useful as it allows the representation of complex systems of linear equations in a very compact form, by using vectors and matrices. That is, an array of numbers together with vectors and the calculation of the terminals make the analysis and even the comprehension of systems of linear equations much easier. This week has been concerned with providing the key ingredients for potential study on matrices, their use and practical applications. The material is by no means meant to be exhaustive. In detail, we went through the basic concepts of a matrix, describing its shape and use. After having introduced the basic concepts, we have been looking at some rules of calculation and manipulation. We saw the idea of equality of matrices, they are transposed, how to add and subtract matrices, how to multiply a matrix by a scalar, how to multiply matrices with each other and how to calculate the inverse of a matrix. We have been focusing on the conditions that must be met for all these manipulations to actually take place. We have been presenting a system of equations using matrix multiplication in the case where the system is linear. Finally, we have provided some examples from business, economics and finance, that have shown the many advantages of using these mathematical tools and practical application to mathematical models. Thank you very much. [MUSIC]