Solving a System of Linear Equations - Wild Linear Algebra A

Explore the fundamentals of solving systems of linear equations in this 49-minute lecture from the Wild Linear Algebra course. Delve into matrix forms, row reduction techniques, elementary row operations, and row echelon forms. Learn how to set up general systems with m equations and n variables, understand matrix-vector multiplication, and apply various formulations including matrix, vector, and linear transformation approaches. Practice row reduction methods using both equations and matrices, and familiarize yourself with key terminology such as augmented matrices, leading entries, and pivot elements. Master the algorithm for row reducing matrices and work through practical examples to solidify your understanding of these essential linear algebra concepts.

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