Solving a System of Linear Equations - Wild Linear Algebra A

Overview

This course on Linear Algebra aims to teach students how to solve general systems of linear equations, understand matrix forms for such systems, perform row reduction, elementary row operations, and recognize row echelon forms. The course covers topics such as defining the product of a matrix by a column vector, linear transformations, vector formulations, and solution strategies. The teaching method includes examples, exercises, and algorithms for row reducing matrices. This course is intended for individuals interested in advancing their knowledge of linear algebra and mathematical problem-solving.

Syllabus

CONTENT SUMMARY: pg 1: @ How to solve general systems of equations; Chinese "Nine chapters of the mathematical art'/C.F.Gauss; row reduction;
pg 2: @ General set_up: m equations in n variables; Matrix formulation; matrix of coefficients;
pg 3: @ 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: @ return to original example; Linear transformation;
pg 5: @ a 3rd way of thinking about our system of linear equations; vector formulation; example;
pg 6: @ example: row reduction working with equations;
pg 7: @ example: row reduction working with matrices; row echelon form mentioned; reduced row echelon form; setting a variable to a parameter;
pg 8: @ Terminology; augmented matrix, leading entry, leading column, row echelon form;
pg 9: @ examples; solution strategy;
pg 10: @ elementary row operations; operations are invertible can be undone; algorithm for row reducing a matrix;
pg 11: @ algorithm for row reducing a matrix; pivot entry;
pg 12: @ example; row reducing a matrix per algorithm;
pg 13: @ exercises 13.1:2;
pg 14: @ exercise 13.3; THANKS to EmptySpaceEnterprise
Introduction
General setup: m equations in n variables
Product of matrix by vector
Equations and row reduction
Terminology echelon forms
Elementary row operations
Row reducing algorithm
Row reduction exercise