Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples

A subspace is a subset that respects the two basic operations of linear algebra: vector addition and scalar multiplication. We say they are “closed under vector addition” and “closed under scalar multiplication”. On a subspace, you can do linear algebra! Indeed, a subspace is an example of a vector space. We see that all of R^n, {0}, and lines through the origin are all subspaces, but that lines NOT through the origin are not subspaces.


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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.


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►How to Watch Math Videos:
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►5 Tips to Make Math Practice Problems Effective: https://www.youtube.com/watch?v=LPH2lqis3D0


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►Discrete Math: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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