MENU

Fun & Interesting

Spanning Sets in Vector Spaces | Linear Algebra

Wrath of Math 13,013 1 year ago
Video Not Working? Fix It Now

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: https://youtu.be/CK65GbUTk4g Linear Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc Join Wrath of Math to get exclusive videos, music, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 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: 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: https://www.patreon.com/join/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: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Math Rap channel: https://www.youtube.com/channel/UCQ2UBhg5nwWCL2aPC7_IpDQ/featured

Comment