Spanning Sets in Vector Spaces | Linear Algebra

Support the production of this course by joining Wrath of Math to access all my Linear Algebra videos plus lecture notes at the premium tier! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out the coolest math clothes in the world! https://mathshion.com/ Linear Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc Get the textbook for this course! https://amzn.to/45KYgmA Business Inquiries: [email protected] 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 ★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 Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Twitter: https://twitter.com/wrathofmathedu 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