We previously saw the "Change of Basis" formula between a nonstandard basis and the standard basis. In this video, we look at how to change between two different nonstandard bases. Indeed, we derive a single matrix, called the Change of Basis Matrix, that is simply the product of two others: converting from the B basis to the standard basis, and converting from the standard basis to the C basis. That lets us go from the B to the C directly.

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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.

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►Discrete Math:    • Discrete Math (Full Course: Sets, Log...  

►Linear Algebra:    • Linear Algebra (Full Course)  

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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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