# A Tutorial Guide to Linear Algebra

This page is currently under construction, and content is added every week as of May 2021.

This textbook is an introduction to linear algebra suitable for senior high-school students who are preparing to enroll in mathematics, engineering, science, and other programs that will require learning some linear algebra. Linear algebra is widely regarded as one of the most challenging mathematics courses in first-year university. Part of the challenge is that often it is a student’s first encounter with abstract mathematics. This textbook is example-oriented, and proceeds from the concrete to the general, step-by-step, so that students see lots of examples and have lots of experience to generalize from before they are faced with abstractions. This textbook may thereby be a bridge for students so that they may better cope with their future very abstract university course in linear algebra. The textbook may also be helpful as a reference for students who are currently taking a university course in linear algebra, as they will be able to dip into this textbook for additional and perhaps more detailed explanations and examples when they run into a difficult spot in their university course.

### Chapter 1: Introduction

1.2 Linear Algebra is Scary, Even for Future Mathematicians. Therefore, be gentle with yourself, hang in there, persist, and in time you too will be able to understand linear algebra and apply it expertly!

### Chapter 2: Lines and their Equations

2.1 Cartesian Coordinates — Lecture notes, Tutorial

2.2 Analytic Geometry — Lecture notes, Tutorial

2.3 Standard Equations of Lines — Lecture notes, Tutorial

2.4 Parametric Equations — Lecture notes, Tutorial

### Chapter 3: Systems of Linear Equations

3.1 Solving $2 \times 2$ Systems of Linear Equations: Basic Methods — Lecture notes, Tutorial

3.2 Solving $2 \times 2$ Systems of Linear Equations: Using Matrices — Lecture notes, Tutorial

3.3 Solving Larger Systems of Linear Equations — Lecture notes, Tutorial

3.4 Some Applications — Lecture notes, Tutorial