Show a Set is Not a Vector Space with the Indicated Operations | Linear Algebra Exercises

To show a set is not a vector space with indicated operations, we must show the set violates at least one of the vector space axioms. We'll do six examples of such problems in this linear algebra video lesson. We'll see some that violate closure of vector addition, closure of scalar multiplication, and more. #linearalgebra Vector Spaces:    • Vector Spaces Explained | Linear Algebra   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 0:23 Problem 1 1:33 Problem 2 3:02 Problem 3 3:49 Problem 4 4:23 Problem 5 5:20 Problem 6 6:22 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