Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra

The fundamental concepts of span, linear combinations, linear dependence, and bases. Help fund future projects: https://www.patreon.com/3blue1brown Thanks to Elo Marie Viennot and Ambros Gleixner from HTW Berlin (www.htw-berlin.de) for contributing German translations and dubbing. Thanks to these viewers for their contributions to translations Arabic: @Cewkins, Hazem Hebrew: Omer Tuchfeld Spanish: Juan Carlos Largo Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown