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9. Image and Kernel

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Nov 1, 2024
58:59

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 π‘‡β„Žπ‘’ π·π‘Žπ‘Ÿπ‘˜ π΄π‘Ÿπ‘‘ π‘œπ‘“ πΏπ‘–π‘›π‘’π‘Žπ‘Ÿ π΄π‘™π‘”π‘’π‘π‘Ÿπ‘Ž. See my website https://bravernewmath.com for more information on my various books: 𝐹𝑒𝑙𝑙 πΉπ‘Ÿπ‘œπ‘›π‘‘π‘Žπ‘™ πΆπ‘Žπ‘™π‘π‘’π‘™π‘’π‘ , π‘‡β„Žπ‘’ π·π‘Žπ‘Ÿπ‘˜ π΄π‘Ÿπ‘‘ π‘œπ‘“ πΏπ‘–π‘›π‘’π‘Žπ‘Ÿ π΄π‘™π‘”π‘’π‘π‘Ÿπ‘Ž, π‘ƒπ‘Ÿπ‘’π‘π‘Žπ‘™π‘π‘’π‘™π‘’π‘  π‘€π‘Žπ‘‘π‘’ 𝐷𝑖𝑓𝑓𝑖𝑐𝑒𝑙𝑑, πΏπ‘œπ‘π‘Žπ‘β„Žπ‘’π‘£π‘ π‘˜π‘– πΌπ‘™π‘™π‘’π‘šπ‘–π‘›π‘Žπ‘‘π‘’π‘‘. 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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9. Image and Kernel | NatokHD