Basics of Linear Algebra

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Basics of Linear Algebra

SAT Score Range

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4 sessions

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This series ended on January 10, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

We will cover the basic ideas required for understanding elementary linear algebra. This includes preliminaries like what a vector and matrix are, how to use Gauss-Jordan elimination to solve systems of equations, determinants, inverse matrices, and more. 

The goal of this short course is to give a solid foundational understanding of the concepts that motivate these mathematical objects, going beyond a strictly formula-based introduction to the concepts you may receive in a pre-calculus or calculus class. I hope students will come away with a great understanding of what ideas like vectors or matrices are about, what motivated them, how they are useful, and what problems they solve.

The motivation for this course is that many first introductions to the topics of matrices and vectors do a poor job of motivating why they're interesting and useful, or why they follow the rules that they do, leaving students confused or feeling like they're just following a set of rules.

The concepts covered will be perfect as a first introduction to the material for anyone planning to take Multivariable Calculus (aka Calculus III), Differential Equations, Linear Algebra, or any course that requires an understanding of vectors and matrices.

Tutored by

Etienne P 🇺🇸

Certified in 2 topics

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Hi, I'm a college sophomore at NC State University studying to become a mathematician. I have a great love for mathematics and an appreciation for its beauty and artistry, and my goal is to spread those same feelings to the students I work with! I love teaching kids of all ages about the joys of math, and it's great to see them be able to succeed with my help!

Schedule

✋ ATTENDANCE POLICY

Each lesson will build off of the last so it is recommended you do not miss any of the sessions. If you do, however, it will not be impossible to follow along and so you are encouraged to still attend if you are interested.

SESSION 1

3

Jan

SESSION 1

Even More Math

Mon 11:30 PM - Tue, 12:50 AM UTCJan 3, 11:30 PM - Jan 4, 12:50 AM UTC

What even is a vector, and what are matrices? Where do they come from, what do they represent, and how do we use them? We'll answer these questions, and derive an important formula by viewing matrices through the lens of linear transformations.

SESSION 2

5

Jan

SESSION 2

Even More Math

Wed 11:30 PM - Thu, 12:50 AM UTCJan 5, 11:30 PM - Jan 6, 12:50 AM UTC

The geometry of linear systems and how to use matrices to solve equations. How can we determine the number of solutions in a system, and what do intersecting planes have to do with lists of numbers? We'll answer this question, and introduce the most basic method of solving a system of linear equations with a matrix: Gauss-Jordan elimination.l

SESSION 3

7

Jan

SESSION 3

Even More Math

Fri 11:30 PM - Sat, 12:50 AM UTCJan 7, 11:30 PM - Jan 8, 12:50 AM UTC

Determinants and Cramer's Rule. We'll introduce the concept of the determinant geometrically and axiomatically, and figure out what we really mean when we say "volume." Then, we'll apply what we've learned about determinants in order to solve systems of equations in a new way with a clever trick known as Cramer's Rule.

SESSION 4

9

Jan

SESSION 4

Even More Math

Sun 11:30 PM - Mon, 12:50 AM UTCJan 9, 11:30 PM - Jan 10, 12:50 AM UTC

The inverse. One of the most important ideas to understand about a matrix is the inverse. What is it, and how do we use it? What's the best way to compute an inverse? When do matrices have inverses, and why is it important to know? We'll answer all these questions and others in our final session on the basics of linear algebra!

Public Discussion

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Jan 3 - Jan 10

1 week

80 mins

/ session

SCHEDULE

Monday, Jan 3

11:30PM

Wednesday, Jan 5

11:30PM

Friday, Jan 7

11:30PM

Sunday, Jan 9

11:30PM