Schoolhouse Hub • Series
Introductory Linear Algebra
BL
IA
Iqra A
This series ended on August 2, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.
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 college freshman majoring in neuroscience, 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 A'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
OT
Session 2
Other Topics
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
OT
Session 3
Other Topics
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
OT
Session 4
Other Topics
DAY 4
We'll talk through the concept of linear transformations and the matrices and graphs of common transformations.
1
Jul
OT
Session 5
Other Topics
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
OT
Session 6
Other Topics
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
OT
Session 7
Other Topics
DAY 7
We'll delve into newer matrix operations and their practical applications.
12
Jul
OT
Session 8
Other Topics
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
OT
Session 9
Other Topics
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
OT
Session 10
Other Topics
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
OT
Session 11
Other Topics
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
OT
Session 12
Other Topics
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
OT
Session 13
Other Topics
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
OT
Session 14
Other Topics
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.