9. Image and Kernel
The image, the kernel, and the rank-nullity theorem. Get 'em while they're hot! This is the 9th in a sequence of videos for a class based on my book πβπ π·πππ π΄ππ‘ ππ πΏπππππ π΄ππππππ. See my website https://bravernewmath.com for more information on my various books: πΉπ’ππ πΉππππ‘ππ πΆππππ’ππ’π , πβπ π·πππ π΄ππ‘ ππ πΏπππππ π΄ππππππ, ππππππππ’ππ’π ππππ π·ππππππ’ππ‘, πΏππππβππ£π ππ πΌπππ’πππππ‘ππ. The first three are available for sale as paperbacks at Amazon, and as pdfs at Lulu. (The Lobachevski book is available at Amazon and the American Mathematical Society) 0:00 Intro 0:30 Row operations preserve linear combinations of columns 9:16 Defining the image 11:00 Defining the kernel 12:03 1st geometric example 18:22 Rank and nullity defined 19:07 2nd geometric example 22:30 Rank-Nullity Theorem 26:51 Quest for a method to find images 43:41 Computing another kernel 47:12 Summary of methods 48:55 Transition to... 49:25 ...the geometry of the kernel
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