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
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.
Download the Guided Notes: Access the guided notes provided with each video. These are available in PDF format for easy download and printing.
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.
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
YouTube Video - How to Study for a Math Exam
Filled in notes available for purchase here!
1. Linear Equations
YouTube Video Free Guided Notes
Solutions to a Linear System with Two Equations and Two Unknowns
Coefficient and Augmented Matrices
Elementary Row Operations, Echelon, and Reduced Echelon Form
Gaussian Elimination and Gauss Jordan Elimination
Consistent and Inconsistent Linear Systems
Linear Combinations and Span
2. Matrix Algebra
YouTube Video Free Guided Notes
Addition, Subtraction, and Multiplication of Matrices
Transpose and Trace of a Matrix
Special Matrices - Triangular, Symmetric, and Diagonal
Inverse of a 2x2 and 3x3 Matrix
Solutions to a Linear System Using Matrix Inversion
3. Transformations
YouTube Video Free Guided Notes
Linear Transformations - Domain and Codomain
Linear Transformations - Standard Matrix
Matrix Transformations - Reflection, Projection, Rotation, Expansion/Contraction
One-To-One and Onto Transformations
4. Determinants
YouTube Video Free Guided Notes
Determinant of a 2x2 Matrix
Determinant of a 3x3 Matrix - Cofactor Expansion, Shortcut, Row Reduction
Properties of Determinants
Cramer’s Rule
5. Vector Spaces
YouTube Video Free Guided Notes
Linear Independence
Basis
Coordinate Vectors
Dimension
Row Space, Column Space, and Null Space
Rank of a Matrix and Rank Theorem
6. Eigenvalues and Eigenvectors
YouTube Video Free Guided Notes
Introduction to Eigenvalues and Eigenvectors
How to Find Eigenvalues
How to Find Eigenvectors and a Basis for an Eigenspace
Similar Matrices
Diagonalization
Complex Eigenvalues and Eigenvectors
7. Orthogonality
YouTube Video Free Guided Notes
Norm of a Vector, Unit Vector, Standard Unit Vector
Distance in R^n
Dot Product
Orthogonality of Vectors
Orthogonal Projection
Linear Combination of Orthogonal Vectors
Gram Schmidt Process
Orthogonal Matrices
Orthogonal Diagonalization