Learn the fundamentals of linear algebra through video lessons and guided notes designed for high school students and beginners. Explore matrices, determinants, matrix inverses, and methods for solving systems of equations through clear step-by-step instruction.

High School Linear Algebra

Linear Algebra Video Lessons with Guided Notes

  • Watch the video lessons for each section.

  • Download the guided notes PDF to follow along as you watch.

  • Engage actively by completing the notes during the lesson.

  • Review your completed notes as a study resource for exams.

1. Introduction to Matrices

Learn the basic structure of matrices, including rows, columns, dimensions, and matrix notation. These lessons provide the foundation needed for all subsequent topics in linear algebra.

  • Introduction to Matrices | Matrix Dimension and Elements Explained

‍ ‍ ▶️ Video ‍📝 Notes

2. Matrix Operations

Explore the fundamental operations that can be performed on matrices. Learn how to add, subtract, multiply, and scale matrices through clear examples and step-by-step instruction.

  • Matrix Addition, Subtraction, and Scalar Multiplication | Examples

▶️ Video ‍📝 Notes

  • Matrix Multiplication Explained | Examples

‍ ‍ ▶️ Video ‍📝 Notes

3. Determinants

  • How to Find the Determinant of a 2×2 Matrix | Step-by-Step Example

‍ ‍ ▶️ Video‍ ‍📝 Notes

  • How to Find the Determinant of a 3×3 Matrix | Step-by-Step Example

‍ ‍ ▶️ Video ‍📝 Notes

4. Matrix Inverses

  • How to Find the Inverse of a 2×2 Matrix | Step-by-Step Example

‍ ‍ ▶️ Video ‍📝 Notes

  • Solving Systems with Matrix Inverses | Step-by-Step Example

‍ ‍ ▶️ Video‍ ‍📝 Notes

5. Solving Systems of Equations

  • Cramer's Rule Explained | Solve Systems Using Determinants

‍ ‍ ▶️ Video ‍📝 Notes

  • Gaussian Elimination Explained | Solve Systems with Row Echelon Form

‍ ‍▶️ Video‍ ‍📝 Notes

  • Gauss-Jordan Elimination Explained | Solve Systems with Reduced Row Echelon Form

‍ ‍ ▶️ Video‍ ‍📝 Notes

Copyright & Usage

© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.

About Dr. Cheryl Hile

Understand The Math was created by Dr. Cheryl Hile, who earned a Ph.D. in Engineering Science and Applied Mathematics from Northwestern University. She has more than 25 years of experience teaching mathematics at the university level, including 20 years at Penn State. The lessons and guided notes on this site are based on materials she developed for her university courses.