The Null Space & Column Space of a Matrix | Algebraically & Geometrically скачать в хорошем качестве

The Null Space & Column Space of a Matrix | Algebraically & Geometrically

To every matrix, there are two natural subspaces: the Null Space of A, and the Column Space of A, denoted Null(A) and Col(A). Col(A) is the range, or all the vectors "hit" by a transformation. It turns out this is equivalent to the span of the columns of A. Null(A) is all the vectors in the domain that are sent to zero by the transformation. We visualize these two subspaces, prove they actually are subspaces, and show how to compute them. ************************************************** 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