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WildLinAlg15: Applications of row reduction (Gaussian elimination) I

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)
Length: 41:38

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