Ace Linear Algebra in 10 Hours (The Complete Course)
Study of lines, planes, and vectors, and the areas and spaces they create
Updated on Jun, 2025
Language - English
Teaching and Academics ,Math,Algebra
Lectures -101
Resources -34
Duration -10 hours
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Course Description
HOW THIS COURSE WORK:
This course, Ace Linear Algebra in 10 Hours (The Complete Course), is intended to introduce the student to the study of lines, planes, and vectors, and the areas and spaces they create. The course includes videos, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:
Vectors
Basic Matrix Algebra
Linear Systems
Subspaces, Linear Spans, and Solution Spaces
Linear Dependence, Basis, and Dimension
Projections and Cross Products
Lines and Planes
Intersections and Distances
Square Matrices
Determinants
CONTENT YOU WILL GET INSIDE EACH SECTION:
Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.
Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).
Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.
THINGS THAT ARE INCLUDED IN THE COURSE:
An instructor who truly cares about your success
Lifetime access to Ace Linear Algebra in 10 Hours (The Complete Course)
HIGHLIGHTS:
#1: Downloadable lectures so you can watch the videos whenever and wherever you are.
#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.
#3: Ten problem sets at the end of each section (with solutions!) for you to do more practice.
#4: Step-by-step guide to help you solve problems.
See you inside the course!
- Gina :)
Goals
- Understand vectors geometrically and algebraically
- Write a vector as a linear combination of other vectors
- Identify in simple cases if a vector is in the span of others
- Compute dot product and cross product of two vectors
- Perform basic matrix operations (sum, scalar multiplication, transpose, matrix multiplication)
- Understand the interpretation of matrix multiplication
- Understand and use Gauss-Jordan and Gaussian Elimination to solve system of linear equations using matrix form
- Determine number of solutions of a linear system
- Understand subspaces in Rn
- Relate the general solution to a non-homogeneous system to the solution of a homogeneous system (nullspace) and the particular solution
- Interchange between a nullspace and generators
- Understand the geometric interpretation of the general solution of a non-homogeneous system
- Identify linear independence and dependency relationship
- Identify the basis and dimension of a set of vectors
- State and understand the Invertibility Theorem
- Understand and perform operations of vectors (projection, cross product, and triple scalar product)
- Study equations and geometric interpretation of lines and planes in R3
- Determine the intersections and distances between lines and planes in R3
- Find the inverse of a square matrix
- Solve a system of linear equations using the inverse of the coefficient matrix
- Find the determinants of larger (n>2) matrices using cofactor expansion and row/column operations
- Solve a system of linear equations using Cramer's Rule
- Find the inverse of a matrix using its adjoint matrix
Prerequisites
- Precalculus (algebra, trigonometry, and functions)
Curriculum
Check out the detailed breakdown of what’s inside the course
Introduction
3 Lectures
-
Overview
02:26
02:26
-
Welcome and How It Works
03:34
03:34
-
Tips to Maximize Your Learning
Vectors
15 Lectures
Basic Matrix Algebra
11 Lectures
Linear Systems
10 Lectures
Subspaces, Linear Spans, and Solution Spaces
9 Lectures
Linear Dependence, Basis, and Dimension
9 Lectures
Projections and Cross Products
7 Lectures
Lines and Planes
6 Lectures
Intersections and Distances
10 Lectures
Square Matrices
10 Lectures
Determinants
9 Lectures
Conclusion
2 Lectures
Instructor Details
Gina Chou
During my undergraduate years, I always looked forward to exams because I was well-prepared and found them rewarding. I know this isn’t the case for everyone, so I'm here to share my knowledge and help make your university journey a bit easier!
A bit about me:
I earned my BSc in Atmospheric Science and Physics, with a minor in Mathematics, from McGill University in 2018. I then completed my MSc in 2019 and my PhD in 2024, both in Physics at the University of Toronto. My research focuses on the impact of wind observations on global predictability, Arctic climate, and weather processes.
Since my second year of undergrad, I’ve gained extensive tutoring experience, working with students at Liberty Tutoring, supporting high school and university students through SUS Peer Tutoring and Saturday Programs, and working with private students both in person and online. I also served as a teaching assistant for math and physics courses at both the undergraduate and graduate levels from 2017 to 2024.
I look forward to seeing you in class!
Gina C.
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