Applications of Row Reduction - Gaussian Elimination I - Wild Linear Algebra A - NJ Wildberger

Overview

This course teaches how to tackle the three main problems of Linear Algebra using the algorithm of row reduction, also known as Gaussian elimination. The learning outcomes include understanding how to invert a linear change of coordinates, compute eigenvalues and eigenvectors of a square matrix, and calculate the determinant of a square matrix. The course covers examples illustrating each problem and introduces the concept of y-sub-i matrix for matrix inversion. The teaching method involves theoretical explanations, examples, and exercises. The intended audience for this course is individuals interested in Linear Algebra and its applications.

Syllabus

CONTENT SUMMARY: pg 1: @ 3 main problems of Linear Algebra;
pg 2: @ Inverting a linear change of coordinates; example;
pg 3: @ example finished; new idea: introduce a y-sub-i matrix; to obtain the inverse of a matrix;
pg 4: @ Theorem concerning an invertible matrix;
pg 5: @ 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 @;
pg 7: @ example2 as a reminder of the physical meaning of an eigenvector equation see WildLinAlg7;
pg 8: @ 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 @;
pg 10: @ 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 @ ;
pg 12: @ exercises 15.1:2 ; invert some systems using row reduction; find inverse matrices;
pg 13: @ exercises 15.3:4 ; find eigenvalues and eigenvectors; compute determinants; THANKS to EmptySpaceEnterprise
Introduction
Inverting a linear change of co - ods
Inverting a square invertible matrix by row reduction
Finding eigenvalues and eigenvectors
The eigenvalue problem using row reduction
How to calculate a determinant
If A is upper triangular then detA= product of diagonal entries
Exercises: invert some systems using row reduction; find inverse matrices
exercises 15.3:4 ; find eigenvalues and eigenvectors; compute determinants