Linear Algebra Exam Review

Prepare for your next linear algebra test or final exam with review videos, practice problems, concept reviews, and exam-style examples covering the major topics in a first course in linear algebra.

Practice Problems

📝 Exam Review Problems (Solved in the Exam Review Videos)

📝 Invertible Matrix Theorem (For Reference)

Exam Review Videos

Part 1 - Linear Systems of Equations

‍▶️ Video

Part 2 - Linear Transformations

‍▶️ Video‍ ‍

Part 3 - Matrix Algebra

‍▶️ Video

Part 4 - Determinants

‍▶️ Video

Part 5 - Vector Spaces

‍▶️ Video

Part 6 - Eigenvalues and Eigenvectors

‍▶️ Video

Part 7 - Orthogonality and Least Squares

‍▶️ Video

Concept and Midterm Review Videos

Part 1 - Linear Systems of Equations

‍▶️ Video

Part 2 - Linear Transformations

‍▶️ Video‍ ‍

Midterm 2 Review

‍▶️ Video

Additional Support

Need extra guidance? Explore these resources to round out your exam preparation.

‍▶️ How to Study for a Math Exam
Learn practical strategies to study efficiently and maximize your score.
▶️ Linear Algebra Course Playlist
Browse the complete collection of lecture videos to review any specific topic from scratch.
‍▶️ Linear Algebra Example Problem Playlist
Browse the complete collection of step-by-step worked examples

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.