11. The Determinant (Part 2: Computation)

Compute determinants by mere row reduction. It's more efficient, more flavorful, and far easier to understand than using cofactor expansion. It's all here under the Big Top: Elementary Matrices, the Row Perspective on Matrix Multiplication, and even a live Transpose! You won't believe your eyes! This is the eleventh in what will eventually be a sequence of supplementary videos for a linear algebra class that I teach based on my book 𝑇ℎ𝑒 𝐷𝑎𝑟𝑘 𝐴𝑟𝑡 𝑜𝑓 𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑙𝑔𝑒𝑏𝑟𝑎. See my website https://bravernewmath.com for more information on my various books: 𝐹𝑢𝑙𝑙 𝐹𝑟𝑜𝑛𝑡𝑎𝑙 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠, 𝑇ℎ𝑒 𝐷𝑎𝑟𝑘 𝐴𝑟𝑡 𝑜𝑓 𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑙𝑔𝑒𝑏𝑟𝑎, 𝑃𝑟𝑒𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑠 𝑀𝑎𝑑𝑒 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡, 𝐿𝑜𝑏𝑎𝑐ℎ𝑒𝑣𝑠𝑘𝑖 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑡𝑒𝑑. 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 1:32 Elementary Matrices 2:58 But Who Cares? A Roadmap... 4:50 Determinants of Elementary Matrices 9:48 Row Ops via Elementary Matrices 14:08 Dumbshow of a Determinant Computation 18:19 The Determinant Algorithm 20:08 A Concrete Example 23:12 Notes on Other Stuff in the Book 25:32 Ye Olde Column and Entry Perspectives on Mx Mult 27:44 The ROW Perspective on Mx Mult 31:31 WHY Rows Ops can be done with Elem Mxs 39:24 WHY the Row Perspective Works