This series ended on August 2, 2022. Any 1:1 and group chats related to this series are disabled 1 week after the last session.

This series is part of Schoolhouse Summer Camp. Explore Summer Camp

### Series Details

About

Linear algebra began as the study of linear systems of equations. Currently, linear systems remain of great importance, in part due to their relative simplicity. For true mastery in any field, from physics to computer science, an understanding of linear algebra is fundamental. One might even argue that linear algebra and its applications are even more important than those of calculus in today's world.

This course provides an introduction to linear algebra from a concrete point of view. We emphasize understanding through intuitive exposition and plenty of examples and applications. Whilst we will need to understand theory, we will focus on the concrete setting of Euclidean space and relegate more abstract ideas such as general vector spaces to a second course.

Co-taught with SHW tutor @Yu Heng L, who also developed the series idea, overview, and outline!

PREREQUISITES

High school Algebra I and II are required. Pre-calculus, trigonometry, and calculus are not necessary.

SYLLABUS

1. Linear Systems (~5 sessions)

2. Matrices (~3 sessions)

3. Determinants (~2 sessions)

4. Eigenvalues and Eigenvectors (~4 sessions)

✋ ATTENDANCE POLICY

Please do your best to show up to all sessions, as all covered concepts build on each other. If possible, let the instructor(s) know ahead of time if you must miss a day so they can help you catch up in a timely manner.

Dates

June 21 - August 2

Learners

30 / 40

Total Sessions

14

### About the Tutor

BL

IA

I'm a rising college freshman with academic interests in biology, chemistry, and the humanities. In my free time, I enjoy reading, writing, drawing, and ranting about the French Revolution!

View Iqra's Profile

### Upcoming Sessions

0

### Past Sessions

14

21

Jun

O

Session 1

#### Orientation

DAY 1

We'll introduce ourselves and our interests in math, as well as what we expect and hope to take away from this series.

We'll introduce the concept of systems of strictly linear equations and the fundamentals of matrix notation. We'll also delve into using row reduction and entry elimination (Gauss-Jordan Elimination) to simplify and solve systems in matrix notation.

23

Jun

M

Session 2

#### Meetup

DAY 2

We'll introduce using row reduction to simplify matrices and two possible and common forms a matrix can take on: echelon form and reduced echelon form.

25

Jun

M

Session 3

#### Meetup

DAY 3

We'll go over common types of vectors, basic matrix operations, types of variables, and consistency. We'll also go over fundamental algebraic properties of matrices. We'll then introduce the most powerful and versatile equation we'll be using in the rest of the series: the matrix equation Ax = b.

28

Jun

M

Session 4

#### Meetup

DAY 4

We'll talk through the concept of linear transformations and the matrices and graphs of common transformations.

1

Jul

M

Session 5

#### Meetup

DAY 5

We'll introduce homogeneous equations and their trivial and non-trivial solutions, writing solutions in parametric form, and linearly independent and dependent vectors.

5

Jul

M

Session 6

#### Meetup

DAY 6

We'll finish up Unit 1 (Linear Systems) by exploring common real-world applications of linear systems and matrices, such as in balancing chemical equations, analyzing traffic flow, and observing population change over time.

8

Jul

M

Session 7

#### Meetup

DAY 7

We'll delve into newer matrix operations and their practical applications.

12

Jul

M

Session 8

#### Meetup

DAY 8

We're halfway through! We'll introduce methods of calculating the inverse of a matrix. We'll also go over the Inverse Matrix Theorem (IVT), which will be crucial to the remainder of the course.

15

Jul

M

Session 9

#### Meetup

DAY 9

We'll walk through factorizing a matrix by its upper and lower triangular forms and how this can help us with more advanced matrix operations in the future.

19

Jul

M

Session 10

#### Meetup

DAY 10

We'll begin unit three by introducing the concept of a matrix determinant, its importance, and different methods of calculating it. We'll also go over some fundamental properties of a determinant.

22

Jul

M

Session 11

#### Meetup

DAY 11

We'll go over different methods of using determinants to solve a system, including Cramer's Rule and the adjoint/adjugate. We'll also use matrices and determinants to calculate the area of a two-dimensional parallelogram and the volume of a three-dimensional parallelepiped.

26

Jul

M

Session 12

#### Meetup

DAY 12

We'll spend this session perusing a more abstract field of linear algebra to understand basic novel concepts and the important roles they will play in the following sessions. We'll go over bases and different types of matrix spaces, and what they can reveal about a matrix.

29

Jul

M

Session 13

#### Meetup

DAY 13

We'll begin our fourth and final unit on eigenvectors and eigenvalues by introducing their concepts and importance, as well as using the Characteristic Equation to relate the two.

2

Aug

M

Session 14

#### Meetup

DAY 14

We'll go over diagonalizing matrices to be able to easily compute high powers of matrices. We'll also introduce Markov chains and stochastic modeling, and then wind down the session with group discussion and series feedback.