Roadmap March 22th - klklklk PDF

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Roadmap for Essential Mathematics for Economists I: Lecture March 22th

Content: In this lecture we will finish Matrix Algebra, which still belongs to Topic 2: Linear Algebra. In the previous weeks you have learn about techniques to solve a system of linear equations. These techniques did not rely on the use of matrix algebra. Today, you are going to learn about the Cramer’s rule, a technique that uses matrix algebra to solve a system of linear equations. You will then learn matrix derivatives. The last podcast will talk about an advanced topic: the Eigenvalue Problem. Until now, we have seen systems of n linear equations in n unknowns. In the last podcast you will learn how to solve the Eigenvalue Problem, which is a specific problem consisting of n equations and n+1 unknowns (the n elements of the eigenvector + the eigenvalue). At the end of the notes that cover the eigenvalue problem you will find notes covering the properties of the eigenvalues/eigenvectors. I do not discuss these properties in the podcast. They are not part of the exam, but they are still useful information. If you choose to have a glance at them and have questions let us know. You will also find notes for sub-topic 2.2.9 – Quadratic Forms. There is no podcast for quadratic forms and the notes mostly contains definitions and theorems. While quadratic forms will not be part of the exam, they are important, so I still encourage you to have a look at them. Podcasts: I have prepared podcasts by sub-topic (see below). For each sub-topic, you will find the podcast and the corresponding lecture notes. I recommend you listen to the podcasts in the following (logical) order: Matrices (folder starting with 2.2): 2.2.6 – Cramer Rule 2.2.7 – Matrix Derivatives 2.2.8 – Eigenvalue Problem

Exercises: Practice questions can be found in the exercise folder....