Wild Linear Algebra 13: Solving a system of linear equations





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Uploaded on Mar 9, 2011

This is the 13th lecture in this course on Linear Algebra. Here we start studying general systems of linear equations, matrix forms for such a system, row reduction, elementary row operations and row echelon forms.

This course is given by Assoc Prof N J Wildberger of UNSW, who also has other YouTube series, including WildTrig, MathFoundations and Algebraic Topology.

CONTENT SUMMARY: pg 1: @00:08 How to solve general systems of equations; Chinese "Nine chapters of the mathematical art'/C.F.Gauss; row reduction;
pg 2: @03:04 General set_up: m equations in n variables; Matrix formulation; matrix of coefficients;
pg 3: @05:50 Defining the product of a matrix by a column vector; 2 propositions used throughout the remainder of course; matrix formulation of basic system of equations;
pg 4: @09:07 return to original example; Linear transformation;
pg 5: @10:49 a 3rd way of thinking about our system of linear equations; vector formulation; example;
pg 6: @14:12 example: row reduction (working with equations);
pg 7: @24:48 example: row reduction (working with matrices); row echelon form mentioned; reduced row echelon form; setting a variable to a parameter;
pg 8: @30:17 Terminology; augmented matrix, leading entry, leading column, row echelon form;
pg 9: @32:07 examples; solution strategy;
pg 10: @35:36 elementary row operations; operations are invertible (can be undone); algorithm for row reducing a matrix;
pg 11: @38:11 algorithm for row reducing a matrix; pivot entry;
pg 12: @43:41 example; row reducing a matrix per algorithm;
pg 13: @47:38 exercises 13.(1:2);
pg 14: @48:02 exercise 13.3; (THANKS to EmptySpaceEnterprise)

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

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