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Insights into Mathematics via YouTube
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
Insights into Mathematics
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