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Applications of row reduction (Gaussian elimination) I | Wild Linear Algebra A 15 | NJ Wildberger

This lecture shows how the three main problems of Linear Algebra can be tackled using the algorithm of row reduction, also called Gaussian elimination. The three main problems are: how to invert a linear change of coordinates, how to compute the eigenvalues and eigenvectors of a square matrix, and how to compute the determinant of a square matrix. Each problem is illustrated with examples. This is one of a series of lectures maing a first course in Linear Algebra, given by Assoc Prof N J Wildberger of UNSW, also the discoverer of Rational Trigonometry. CONTENT SUMMARY: pg 1: @00:08 3 main problems of Linear Algebra; pg 2: @01:51 Inverting a linear change of coordinates; example; pg 3: @05:19 example finished; new idea: introduce a y-sub-i matrix; to obtain the inverse of a matrix; pg 4: @09:17 Theorem concerning an invertible matrix; pg 5: @11:00 Finding eigenvalues and eigenvectors of an nXn matrix; remark about the Homogeneous case; g 6: @14:23 The eigenvalue problem using row reduction; example1; check of result @19:34; pg 7: @20:34 example2 as a reminder of the physical meaning of an eigenvector equation (see WildLinAlg7); pg 8: @24:38 example2 continued; finding the eigenvectors using row reduction; perpendicular eigenvectors; pg 9: @27:52 How to calculate a determinant; characteristics of a determinant; as the volume of a parallelpiped; properties of a determinant necessary to do row reduction @30:20; pg 10: @31:32 the determinant of an upper triangular matrix; pg 11: @35:11 example: putting a matrix in upper triangular form to obtain its determinant; remark about this lesson @38:47 ; pg 12: @39:33 exercises 15.(1:2) ; invert some systems using row reduction; find inverse matrices; pg 13: @40:17 exercises 15.(3:4) ; find eigenvalues and eigenvectors; compute determinants; (THANKS to EmptySpaceEnterprise) Video Chapters: 00:00 Introduction 01:50 Inverting a linear change of co - ods 09:17 Inverting a square invertible matrix by row reduction 11:00 Finding eigenvalues and eigenvectors 14:23 The eigenvalue problem using row reduction 27:51 How to calculate a determinant 31:32 If A is upper triangular then det(A)= product of diagonal entries 39:33 Exercises: invert some systems using row reduction; find inverse matrices 40:17 exercises 15.(3:4) ; find eigenvalues and eigenvectors; compute determinants ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист