Lesson 8: Solving Systems of Linear Equations
Preview
Every item you buy (clothes, food, etc.) requires multiple raw materials to produce. Those raw materials are sourced from sectors of the economy that are constantly exchanging and trading their good and services with each other. In this lesson we’ll study a simplified model of how goods are exchanged in an economy. The goal will be to understand how raw materials flow between different sectors in the economy. The exchange model we will study will yield a system of linear equations with multiple unknowns. We’ll then spend the rest of the lesson studying linear systems in general, introducing matrices and vectors to describe how to formulate and solve such systems.
In Module I we’ll learn how to translate back and forth between a system of linear equations and its matrix representation, and define matrices and vectors.
In Module II we’ll discuss how to solve a system of linear equations in matrix form using “augmented matrices” and “elementary row operations.”
Review
Learn
Work through the lesson notes below, consulting the videos below it when you get to the "See Class Notes" boxes. For your records, the annotated lesson notes are below the videos. Some tips for you as you work through these resources:
I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.
Lesson Notes
Lesson 8.pdfClass Notes A
Class Notes B
Class Notes C
Class Notes D
Class Notes E
Class Notes F
Reflect
If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:
Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.
Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.
If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:
Please summarize the main mathematical takeaways from the lesson notes.
What was the most interesting part of what you learned, and why?
What, if anything, do you still find confusing?
Practice
Work through the practice problems suggested below to see how much of this lesson you've understood.
Lesson 8 - Practice Problems.pdf