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.

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.

View New Edited Version: https://youtu.be/ysZvGnZgfgQ This video explains how to determine the surface area of a plane over a circular region in the xy plane using polar coordinates. http://mathispower4u.com

Amazing, Life Changing Tutor
Before I met Jonathan, I was struggling through most of my STEM classes because I was simply not studying properly. He taught me all kinds of new study habits that would help me to save time, raise my grades, and lower my stress. Jonathan was specifically tutoring me in vector calculus and is an amazing tutor on the subject. You will walk away from a lesson with a gameplan knowing exactly what you need to do before your next session with him or before your next exam in order to do well in the course. I highly recommend him as a tutor.

This video will show you how the method of partial fraction decomposition can break down a fraction into smaller fractions. Remember to carefully identify your factors as either linear or quadratic, this will really help you identify what to put in the numerator of each fraction. To find the missing coefficents use Gauss Jordan elimination…

Amazing, Life Changing Tutor
Before I met Jonathan, I was struggling through most of my STEM classes because I was simply not studying properly. He taught me all kinds of new study habits that would help me to save time, raise my grades, and lower my stress. Jonathan was specifically tutoring me in vector calculus and is an amazing tutor on the subject. You will walk away from a lesson with a game plan knowing exactly what you need to do before your next session with him or before your next exam in order to do well in the course. I highly recommend him as a tutor.