Understanding Matrices and Matrix Notation

When people think of "cavemen", they are typically thinking of Neanderthals, not just because they were so similar to us, but also because they were the first extinct hominins ever discovered in the 19th century. We have learned quite a lot about these hominins since their discovery, how they differ from us, and what their demise must have been. We have also learned about a similar group called Denisovans. What is the relationship between these hominins and ourselves?Script by Erika of Gutsick Gibbon: https://www.youtube.com/c/GutsickGibbonWatch the whole Anthropology playlist: http://bit.ly/ProfDaveAnthroGeneral Chemistry Tutorials: http://bit.ly/ProfDaveGenChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioAnatomy & Physiology Tutorials: http://bit.ly/ProfDaveAnatPhysMicrobiology Tutorials: http://bit.ly/ProfDaveMicrobioBotany Tutorials: http://bit.ly/ProfDaveBotanyZoology Tutorials: http://bit.ly/ProfDaveZooEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

Moving on, we reach the Late Middle Ages, which was a tumultuous time. It included events like the Hundred Years' War and the Black Death. Here we see the first initial signs of a public distrust in the Church which eventually led to the Renaissance. Let's get a closer look.Script by Peter WyetznerWatch the whole World History playlist: http://bit.ly/ProfDaveWorldHistoryAmerican History Tutorials: http://bit.ly/ProfDaveAmericanHistoryItalian Tutorials: http://bit.ly/ProfDaveItalianClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2General Chemistry Tutorials: http://bit.ly/ProfDaveGenChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Learn more about your ad choices. Visit megaphone.fm/adchoices

We know about functions, so what are inverse functions? Let's find out!Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMathClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2General Chemistry Tutorials: http://bit.ly/ProfDaveGenChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start with some basics.Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMathClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2General Chemistry Tutorials: http://bit.ly/ProfDaveGenChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

What are these funky little dunce caps with the pom pom on top? It's an epoxide! Three-membered rings are neat, and they do lots of stuff. Check it out.Watch the whole Organic Chemistry playlist: http://bit.ly/ProfDaveOrgChemGeneral Chemistry Tutorials: http://bit.ly/ProfDaveGenChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2Mathematics Tutorials: http://bit.ly/ProfDaveMathEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

Check out "The Book" here for 10% off: https://bit.ly/3Z6QTBB Use code: PROFESSORDAVE10The Book: The Ultimate Guide to Rebuilding a Civilization by Hungry Minds is a luxury coffee table book packed with handmade illustrations and mind-expanding ideas. If you’re into unique gifts, premium books, or just love going down rabbit holes, this one’s for you.Remember Bart Sibrel, the worthless fraud who has spent his entire adult life spreading lies denying the achievements of the Apollo missions in sending humans to the lunar surface? And who should only be remembered as that guy Buzz Aldrin punched in the face one time? Well he's back for more punishment! He went on Piers Morgan and humiliated himself. Then astronaut Charlie Duke said some stuff, as well as William Shatner for some reason. Let's watch and laugh together!Debunking Bart Part 1: https://youtu.be/o5LBAepwBfcDebunking Bart Part 2: https://youtu.be/BXOgYRa9mX8Watch my other debunks/debates/discussions: http://bit.ly/ProfDaveDebunkEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Learn more about your ad choices. Visit megaphone.fm/adchoices

Let's continue looking at second declension nouns. We mentioned that most of these are masculine nouns, but there are some exceptions. Let's look at those exceptions now!Script by Patrizia Farina, Professor of Italian at Western Connecticut State University and Purchase College.Watch the whole Latin playlist: http://bit.ly/ProfDaveLatinItalian Tutorials: http://bit.ly/ProfDaveItalianAmerican History Tutorials: http://bit.ly/ProfDaveAmericanHistoryPhilosophy Tutorials: http://bit.ly/ProfDavePhiloClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2General Chemistry Tutorials: http://bit.ly/ProfDaveGenChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

Which thing gets oxidized, the oxidizing agent? No wait, that's what gets reduced, or is it the reducing agent? Ahh! Stupid binary concepts! OK, settle down. Watch this clip and learn everything you need to know about electron transfer.Watch the whole General Chemistry playlist: http://bit.ly/ProfDaveGenChemStudy for the AP Chemistry exam with me: https://bit.ly/ProfDaveAPChemOrganic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2Mathematics Tutorials: http://bit.ly/ProfDaveMathsEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

We know how to make enolates, but when two structurally different enolates are possible, how do we get the one we want? It has to do with selecting the right base. In explaining this, we will also discuss the difference between thermodynamic vs. kinetic control during a reaction.Watch the whole Organic Chemistry playlist: http://bit.ly/ProfDaveOrgChemGeneral Chemistry Tutorials: http://bit.ly/ProfDaveGenChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2Mathematics Tutorials: http://bit.ly/ProfDaveMathEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices

Well, this is weird. What are all these squiggles? Those peaks represent the wavelengths of infrared light that don't get to the detector, because there's some functional group in the sample absorbing them. Professor Dave busts out some dance moves in this one. Do the symmetric stretch!Watch the whole Organic Chemistry playlist: http://bit.ly/ProfDaveOrgChemGeneral Chemistry Tutorials: http://bit.ly/ProfDaveGenChemBiochemistry Tutorials: http://bit.ly/ProfDaveBiochemBiology Tutorials: http://bit.ly/ProfDaveBioClassical Physics Tutorials: http://bit.ly/ProfDavePhysics1Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2Mathematics Tutorials: http://bit.ly/ProfDaveMathEMAIL► [email protected]► http://patreon.com/ProfessorDaveExplainsCheck out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!Amazon: https://amzn.to/2HtNpVHBookshop: https://bit.ly/39cKADMBarnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT Learn more about your ad choices. Visit megaphone.fm/adchoices