Linear Algebra Review

Videos and

Guided Notes

Welcome to our Linear Algebra Review Videos and Guided Notes page! This resource is designed to help you revisit and strengthen your understanding of fundamental linear algebra concepts. Whether you're preparing for exams, brushing up on your skills, or seeking a deeper comprehension of linear algebra, our materials are here to support you.

What You'll Find Here

Concise Review Video Lessons
Our linear algebra review videos cover essential topics and concepts in a clear and concise manner. Each video is structured to provide straightforward explanations, practical examples, and step-by-step solutions. These videos are perfect for a quick review or for reinforcing your understanding of key concepts.

Interactive Guided Notes
To complement our videos, we offer downloadable guided notes. These notes are designed to be filled in as you watch the videos, ensuring active engagement with the material. Guided notes help you to:

  • Reinforce Understanding: By filling in key information as you review, you solidify your grasp of linear algebra concepts.

  • Enhance Retention: Active note-taking aids in embedding the information in your memory.

  • Organize Your Study Materials: Keep your notes well-organized and easily accessible for future review and exam preparation.

How to Use These Resources

  1. Watch the Videos: Begin by watching our linear algebra review videos. Each lesson is designed to build on your existing knowledge and clarify complex topics.

  2. Download the Guided Notes: Access the guided notes provided with each video. These are available in PDF format for easy download and printing.

  3. Follow Along and Fill In: As you watch the videos, fill in the guided notes. This process will help you engage with the material and retain the information more effectively.

  4. Review and Study: Use your completed notes as a valuable study aid for reviewing key concepts and preparing for exams.

Notes Available for Purchase

For those who prefer a completed set of notes, we offer filled-in versions of our guided notes available for purchase in our store. These notes provide all the key information in a well-organized format, perfect for quick reference and review. Visit our store to explore the options and find the notes that best suit your needs.

Start Reviewing Today!

Dive into our linear algebra review videos and guided notes to reinforce your understanding and boost your confidence. Click on the links below to access the content and start mastering linear algebra with ease.

Topics Covered

Filled in notes available for purchase here!

1. Linear Equations

YouTube Video Free Guided Notes

  1. Solutions to a Linear System with Two Equations and Two Unknowns

  2. Coefficient and Augmented Matrices

  3. Elementary Row Operations, Echelon, and Reduced Echelon Form

  4. Gaussian Elimination and Gauss Jordan Elimination

  5. Consistent and Inconsistent Linear Systems

  6. Linear Combinations and Span

2. Matrix Algebra

YouTube Video Free Guided Notes

  1. Addition, Subtraction, and Multiplication of Matrices

  2. Transpose and Trace of a Matrix

  3. Special Matrices - Triangular, Symmetric, and Diagonal

  4. Inverse of a 2x2 and 3x3 Matrix

  5. Solutions to a Linear System Using Matrix Inversion

3. Transformations

YouTube Video Free Guided Notes

  1. Linear Transformations - Domain and Codomain

  2. Linear Transformations - Standard Matrix

  3. Matrix Transformations - Reflection, Projection, Rotation, Expansion/Contraction

  4. One-To-One and Onto Transformations

4. Determinants

YouTube Video Free Guided Notes

  1. Determinant of a 2x2 Matrix

  2. Determinant of a 3x3 Matrix - Cofactor Expansion, Shortcut, Row Reduction

  3. Properties of Determinants

  4. Cramer’s Rule

5. Vector Spaces

YouTube Video Free Guided Notes

  1. Linear Independence

  2. Basis

  3. Coordinate Vectors

  4. Dimension

  5. Row Space, Column Space, and Null Space

  6. Rank of a Matrix and Rank Theorem

6. Eigenvalues and Eigenvectors

YouTube Video Free Guided Notes

  1. Introduction to Eigenvalues and Eigenvectors

  2. How to Find Eigenvalues

  3. How to Find Eigenvectors and a Basis for an Eigenspace

  4. Similar Matrices

  5. Diagonalization

  6. Complex Eigenvalues and Eigenvectors

7. Orthogonality

YouTube Video Free Guided Notes

  1. Norm of a Vector, Unit Vector, Standard Unit Vector

  2. Distance in R^n

  3. Dot Product

  4. Orthogonality of Vectors

  5. Orthogonal Projection

  6. Linear Combination of Orthogonal Vectors

  7. Gram Schmidt Process

  8. Orthogonal Matrices

  9. Orthogonal Diagonalization