Visualizing Composition of Linear Transformations **aka Matrix Multiplication**

Matrix multiplication is an algebraic operation. But we cared about that algebraic operation because it represented a core geometric idea: the composition of linear transformations. In this video I introduce my favorite way to visualizing Linear Transformations in 2D (dynamically!). We then can visualizing the composition and track what happens algebraically at the level of linear combinations or at the level of matrix multiplication. Typo: The yellow unit vector should be (0,1) not (1,0) ************************************************** Now it's your turn: 1) Summarize the big idea of this video in your own words 2) Write down anything you are unsure about to think about later 3) What questions for the future do you have? Where are we going with this content? 4) Can you come up with your own sample test problem on this material? Solve it! Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master math means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK. *************************************************** ►Want more ideas for learning math effectively? How to Watch Math Videos:    • How to watch math videos   ►5 Tips to Make Math Practice Problems Effective:    • 5 Tips To Make Math Practice Problems Actu...   **************************************************** ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   **************************************************** Course Playlists: ►Calculus I:    • Calculus I (Limits, Derivative, Integrals)...   ►Calculus II:    • Older Calculus II (New Playlist For Spring...   ►Discrete Math:    • Discrete Math (Full Course: Sets, Logic, P...   ►Linear Algebra:    • Linear Algebra (Full Course)   ***************************************************** ►Follow me on Twitter:   / treforbazett   ***************************************************** This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett