We go over six examples of showing a set of vectors is linearly independent or not linearly independent. We do this by seeing if vectors are multiples of each other, linear combinations of each other, and ultimately by using Gauss-Jordan or determinants to make conclusions about homogenous linear systems. #linearalgebra

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

Join Wrath of Math to get exclusive videos, music, and more:
   / @wrathofmath  

0:00 Intro
0:19 Definition of Linear Independence
0:34 Are the 2 Vectors in R^3 Linearly Independent?
1:18 Are the 3 Vectors in R^2 Linearly Independent?
2:44 Are the 2 Vectors in R^3 Linearly Independent?
3:47 Are the 2 Matrices in M22 Linearly Independent?
4:26 Linear Independence Theorem
5:04 Are 3 Vectors in R^3 Independent?
6:19 Gauss-Jordan to Show Linear Independence
6:45 Determinant to Show Linear Independence
7:44 Are 4 Vectors in R^4 Independent?
8:34 Gauss-Jordan to Show Linear Independence
9:26 Determinant to Show Linear Independence
9:44 Conclusion

◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Abstract Algebra: https://amzn.to/3IjoZaO
Linear Algebra: https://amzn.to/43xAWEz
Calculus: https://amzn.to/3PieD1M
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd

★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons  
◆ Donate on PayPal: https://www.paypal.me/wrathofmath

Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!

Outro music is mine. You cannot find it anywhere, for now.

Follow Wrath of Math on...
● Instagram:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu  

My Math Rap channel:    / @mathbars2020