Spanning Sets in Vector Spaces | Linear Algebra

We give a thorough overview of spanning sets and spans in linear algebra. We define spanning sets, what it means for one set to span another, and review linear combinations. We'll see examples and nonexamples of spanning sets, take a geometric perspective, and see how to show a set of vectors in R^n spans R^n. #linearalgebra
Gauss-Jordan Elimination: • Guide to Gauss-Jordan ...
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
0:50 Definition of Spanning Set
2:51 Spanning Set of R^n
4:34 Geometric View of Spans
6:01 Spanning Set of Polynomials
7:19 Two Important Problems Related to Spanning
7:55 Show a Vector is a Linear Combination of a Set of Vectors
9:38 Show a Vectors isn't a Linear Combination of a Set of Vectors
10:48 Show a Set of Vectors Spans R^3
12:33 Show a Set of Vectors Doesn't Span R^3
13:40 Geometric Explanation
14:26 Conclusion
◉Textbooks I Like◉
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Abstract Algebra: amzn.to/3IjoZaO
Linear Algebra: amzn.to/43xAWEz
Calculus: amzn.to/3PieD1M
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/3tsaEER
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons
◆ Donate on PayPal: 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

[@talastra]

This was one of those times when the example was crucial to understanding (or grasping) the definition finally. Thanks!

[@WrathofMath]

Thanks for watching!

[@talastra]

@@WrathofMath Thanks for making the content to watch, of course.

[@pheinex]

Amazing ❤ Can you make a video for sum and direct sum And thanks

[@SzTz100]

Great video, I really like your rapping at the end.

[@WrathofMath]

Thank you!

[@user-im3eg4vj3g]

GooD I froom iraq

[@WrathofMath]

Thank you!