Linear Independence in Vector Spaces | Linear Algebra

We introduce linearly independent sets of vectors, giving a definition, motivation, examples and nonexamples, and see how to determine if a set of vectors in R^n is linearly independent or linearly dependent using Gauss-Jordan elimination or the determinant. #linearalgebra
Determine if a Set is Linear Independent (members only): • Determine if a Set of ...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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0:00 Intro
0:19 Motivation
3:50 Definition of Linearly Independent Set of Vectors
4:59 How we Show a Set is Linearly Independent
6:00 Linearly Independent Vectors in R^n
7:38 Showing a Set of Vectors in R^3 is Linearly Independent
10:59 Review
11:50 Conclusion
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[@rp101aquatics6]

This was conveniently posted 2 days before my exam. Thank you this entire series has been a valuable study tool.

[@WrathofMath]

Glad to help! You're here before the video is even officially published with a thumbnail haha - that's how I know you're using the playlist! Good luck on the exam!

[@rp101aquatics6]

@@WrathofMath thank you! This exam is most likely getting dropped since I have a 108 exam average but it never hurts to excel. This series utilizes the exact same textbook that my course is based off of so it works out brilliantly.

[@rp101aquatics6]

@@WrathofMath Do you have any videos on coordinates and basis? I think its the only topic on the exam that I am yet to conquer

[@WrathofMath]

I actually skipped over that topic to make the eigenvectors and eigenvalues video because I didn't feel like making the coordinates and basis lessons yet haha. I will soon, but sounds like you have the course in the bag!

[@henrywoo1668]

Thank you sir for your very clear explanation !

[@WrathofMath]

Thanks for watching!

[@talastra]

The motivation part is very helpful. My brain locks up on things like, if Ax = 0 then there are nontrivial solutions ... if the determinant is trivial (zero) there are non trivial solutions. Ack.

[@WrathofMath]

Thanks for watching and the comment! All the equivalences in linear algebra can definitely by overwhelming at times, feels like we're making wild leaps from one thing to another when using some equivalences. Proofs of all the common equivalences we use, for what it's worth, will be provided in this course eventually. I will insert them in their proper place in the playlist, but I am skipping a lot of proofs for now as I'm trying to finish the core parts of the series ASAP, and I know a lot of people aren't searching up the proofs, they're searching for all the meaty process-oriented stuff.