Inverting 3x3 Matrices - Wild Linear Algebra A | NJ Wildberger

Overview

Explore the fundamental concepts of inverting 3x3 matrices in this comprehensive 46-minute lecture from the Wild Linear Algebra series. Delve into the importance of determinants and their relation to tri-vectors, learn various methods for obtaining determinants, and master the process of solving 3x3 linear systems. Discover the 3x3 inversion theorem, understand the definition and significance of matrix minors and adjoints, and examine the relationship between inverse, determinant, and adjoint matrices. Practice with examples, study 3x3 matrix operations, and grasp why the inverse law works. Investigate properties of 3x3 matrices, explore invertible matrices, and prove an important proposition about the product of invertible matrices. Conclude with exercises to reinforce your understanding of these crucial linear algebra concepts.

Syllabus

CONTENT SUMMARY: pg 1: @ How to invert the change in coordinates; 3x3 matrix; 2x2 review;
pg 2: @ importance of the determinant; determinant relation to tri-vectors;
pg 3: @ different ways of obtaining the determinant;
pg 4: @ solving the 3x3 linear system;
pg 5: @ solving the system continued;
pg 6: @ 3x3 inversion theorem derived;
pg 7: @ notation to help remember the 3x3 inversion formula; definition of the minor of a matrix;
pg 8: @ Definition of the adjoint of a matrix; relationship of the inverse, determinant and adjoint of a matrix;
pg 9: @ examples; determination of the adjoint; determination of the inverse; matrix times its inverse; the identity matrix;
pg 10: @ example;
pg 11: @ 3x3 matrix operations;
pg 12: @ why the inverse law works; properties of a 3x3 matrix; an invertible matrix;
pg 13: @ Proposition: If 2 matrices are invertible then so is their product, and the inverse of the product is equal to the product of their inverses rearranged; proof;
pg 14: @ exercises 8.1:2 ;
pg 15: @ exercises 8.3:4 ; THANKS to EmptySpaceEnterprise
Introduction
importance of the determinant
different ways of obtaining the determinant
Theorem 3×3 inversion
Definition of the adjoint of a matrix
3×3 matrix operations
why the Inverse law works
Proposition