Worksheet 6 - Module 3 - Lecture-by-Lecture to-do-list

Econ 1540 Module 3 - complete by end of week 11 – In the last module, we introduce the tools of linear algebra. Linear algebra teaches us the tools to handle more than one number at a time. It allows us to add, subtract, scale large arrays of data at once. For economists who handle (potentially large amounts of) data, that’s very useful! Traditionally, matrices were introduced as coefficients in a system of equations. However, with the advent of computers, we no longer need to manipulate coefficient matrices by hand to solve systems of equations. In addition, with progressing digitalization economists have access to ever more data and the use of matrices has shifted from coefficient matrices to (panel) data. So we will introduce vectors and matrices in that manner, and study systems of equations as one (of several) application(s). Permutations and their sign (lecture 8B) Terminology  Head to https://www.statlect.com/matrix-algebra/sign-of-a-permutation Glance over these pages. Identify and jot down words you don’t know or words that appear to be key.  Make a list of the terminology.  Practice and learn the terminology. Learn  Read through https://www.statlect.com/matrix-algebra/sign-of-a-permutation What are the key concepts? What’s the most puzzling? Practice Work through (with pencil and paper) the examples worked out in the text on  The website https://www.statlect.com/matrix-algebra/sign-of-a-permutation Ask questions during office hours if there’s anything in those examples that’s not clear. Solve the following practice questions  Solve the three exercises at the bottom of https://www.statlect.com/matrix-algebra/sign-of-a-permutation Check your answers against the solution provided on the website. Ask questions during office hours if there’s anything about the questions/ answers that’s not clear.

Vectors and Matrices: Batch processing numbers (lecture 9) Terminology  Glance over chapters 15.7, jot down all cursive words. (Vectors) Think of vectors as multiple-numbers-at-once handling, e.g., value of a house over multiple years.  Glance over chapters 15.8. and 15.9, and jot down all cursive words. (Geometry of vectors)  Glance over chapters 15.2. and 15.5, and jot down all cursive words. (Matrices) Think of matrices as multiple-vectors-at-once handling, e.g., value-across-years vectors of several houses.  Make a list of the terminology.  Practice and learn the terminology. Learn  Read through chapter 15.7, (even if not everything is clear). (Vectors) Note: The dot produce of two vectors is a number! (p. 609)  Read through chapters 15.8. and 15.9, (even if not everything is clear). (Geometry of vectors) Make sure to understand orthogonality (p. 614). Note lines/hyperplanes can be constructed as linear combinations (see (15.9.1)) of or as being orthogonal to give vectors (see (15.9.5)).  Read through chapters 15.2. and 15.5, (even if not everything is clear). (Matrices) What are the key concepts? What’s the most puzzling? Practice Work through (with pencil and paper) the examples worked out in the text on  p. 610 (Vectors)  p. 618-620 (Geometry of vectors) Pay particular attention to example 15.9.2. Can you cover the solution and answer the question without looking at the solution?  p. 584-587  p. 599-600 (Matrices) Pay particular attention to example 15.2.6. Can you cover the solution and answer the question without looking at the solution? Ask questions during office hours if there’s anything in those examples that’s not clear. Solve the following practice questions Vectors  p. 610, #1  p. 610, #2  p. 611, #3  p. 611, #6  p. 611, #8  p. 611, #9 Geometry of vectors  p. 616, #2  p. 616, #4  p. 620, #1 (“Find the equation for…”)  p. 620, #2 (“The line ° is given …”)

System of Linear Equations (SLE) and Determinants (lecture 11) Terminology  Glance over chapters 15.1. and 15.6, jot down all cursive words. (SLE)  Glance over chapters 16.1. and 16.2, and jot down all cursive words. (2x2, 3x3 Determinants)  Glance over chapters 16.3. and 16.4, and jot down all cursive words. (Determinants, properties)  Make a list of the terminology.  Practice and learn the terminology. Learn  Read through chapters 15.1. and 15.6, (even if not everything is clear). (SLE)  Read through chapters 16.1. and 16.2, (even if not everything is clear). (2x2, 3x3 Determinants)  Read through chapters 16.3. and 16.4, (even if not everything is clear). (Determinants, properties) What are the key concepts? What’s the most puzzling? Practice Work through (with pencil and paper) the examples worked out in the text on  p. 582  p. 591 (bottom)  p. 602-606 (SLE)  p. 624-625  p. 629-630 (2x2, 3x3 Determinants)  p. 634  p. 637-638 (Determinants, properties) Ask questions during office hours if there’s anything in those examples that’s not clear. Solve the following practice questions System of Linear Equations  p. 583, #1  p. 583, #2  p. 607, #1  p. 607, #3  p. 607, #4  Determinants of 2x2 and 3x3 matrices  p. 626, #1  p. 626, #3  p. 626, #4 (Yes, it’s repeated)  p. 626, #5  p. 626, #7  p. 631, #1  p. 631, #2  p. 631, #3 (a)  p. 632, #5 General determinants and their properties  p. 635, #1  p. 635, #3  p. 639, #1  p. 639, #3  p. 639, #5  p. 639, #6 Check your answers against the solutions in the back of the book or on the respective website. Ask questions during office hours if there’s anything about the questions/ answers that’s not clear. Challenge 2: Learn to calculate determinants