Uploaded May 2020 | Updated September 2026, 1 week ago
We know how to write 1/(1-x) as a geometric series, which is an infinite sum. But we can actually expand it as an infinite product as well!
Check out more calculus problems here: youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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Music: C418 - Pr Department
We know how to write 1/(1-x) as a geometric series, which is an infinite sum. But we can actually expand it as an infinite product as well!
Check out more calculus problems here: youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
New math videos every Monday and Friday. Subscribe to make sure you see them!
Music: C418 - Pr Department
![Matrix Invertibility With F[x]-Modules](https://i.ytimg.com/vi/xnZ2d6y8JmA/mqdefault.jpg "Matrix Invertibility With F[x]-Modules
Characteristic polynomial explanation: https://youtu.be/jCt6mR3QtPk
Ring & Module Theory playlist: https://youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7
In this video, we use F[x]-modules to prove that a matrix is invertible if and only if its determinant is nonzero. Another example of how F[x]-modules can be applied to a ton of things in linear algebra!
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Music: OcularNebula - The Lopez")
