Strengthen your

Linear Algebra Skills

with Videos

and Guided Notes

Welcome to your go-to resource for reviewing key linear algebra concepts! Whether you’re preparing for exams, refreshing your knowledge, or solidifying your understanding, our concise videos and guided notes are here to help you succeed.

What You'll Find Here

Concise Video Lessons
Our linear algebra review videos focus on the essentials, offering:

  • Clear Explanations: Simplify complex topics with straightforward guidance.

  • Practical Examples: See how concepts apply through relevant examples.

  • Step-by-Step Solutions: Learn effective problem-solving techniques in a concise format.

Perfect for quick reviews or reinforcing foundational knowledge, these videos ensure you stay on track.

Interactive Guided Notes
Boost your learning with downloadable guided notes designed to complement each video. These notes help you:

  • Reinforce Understanding: Actively engage with the material by filling in key details.

  • Enhance Retention: Strengthen memory through hands-on note-taking.

  • Stay Organized: Keep all your study materials in one easy-to-review format.

How to Use These Resources

  1. Watch the Videos: Start with our focused linear algebra lessons to revisit essential concepts.

  2. Download Guided Notes: Access the PDF notes linked with each video for easy use.

  3. Engage Actively: Fill in the notes as you watch to deepen your comprehension and retention.

  4. Review and Study: Use your completed notes as a valuable resource for exam prep and review.

Completed Notes Available

Prefer ready-to-use materials? Visit our store for filled-in guided notes, offering a complete set of key information in a well-organized format—perfect for quick reference and efficient study sessions.s.

Start Reviewing Today!

Reinforce your linear algebra knowledge with our videos and guided notes. Click the links below to access the content and build your confidence in linear algebra today!

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