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Linear Algebra

The University of New South Wales,

Updated On 02 Feb, 19

Overview

This course on Linear Algebra is meant for first year undergraduates or college students. It presents the subject in a visual geometric way, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine algebraic geometry. Flexibility in choosing coordinate frameworks is essential for understanding the subject. Determinants also play an important role, and these are introduced in the context of multi-vectors in the sense of Grassmann. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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Lecture 13: WildLinAlg13 Solving a system of linear equations

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Lecture Details

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 @0008 How to solve general systems of equations; Chinese "Nine chapters of the mathematical artC.F.Gauss; row reduction;
pg 2 @0304 General set_up m equations in n variables; Matrix formulation; matrix of coefficients;
pg 3 @0550 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 @0907 return to original example; Linear transformation;
pg 5 @1049 a 3rd way of thinking about our system of linear equations; vector formulation; example;
pg 6 @1412 example row reduction (working with equations);
pg 7 @2448 example row reduction (working with matrices); row echelon form mentioned; reduced row echelon form; setting a variable to a parameter;
pg 8 @3017 Terminology; augmented matrix, leading entry, leading column, row echelon form;
pg 9 @3207 examples; solution strategy;
pg 10 @3536 elementary row operations; operations are invertible (can be undone); algorithm for row reducing a matrix;
pg 11 @3811 algorithm for row reducing a matrix; pivot entry;
pg 12 @4341 example; row reducing a matrix per algorithm;
pg 13 @4738 exercises 13.(12);
pg 14 @4802 exercise 13.3; (THANKS to EmptySpaceEnterprise)