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Insights into Mathematics via YouTube
CONTENT SUMMARY: pg 1: @ inverting the relationship between two pairs of variables;
pg 2: @ application of change of coordinates;
pg 3: @ changing coordinates is related to solving a system of linear equations; a family of problems
pg 4: @ example with parallel lines; zero determinant then 2 lines parallel 2-dim;
pg 5: @ Vector interpretation of a linear system;
pg 6: @ example of 2 vector system without solution;
pg 7: @ change of coordinants as heart of the subject;
pg 8: @ generalize the example on the previous page;
pg 9: @ matrix notation; a column vector; matrix/vector multiplication;
pg 10: @ writing a pair of linear equations in matrix/vector form;
pg 11: @ arithmetic with matrices and vectors; introducing notation independent of application; you might think of this page as the start of a course in linear algebra; column vectors, scalar multiplication, addition, subtraction; approach is independent of any geometric interpretation;
pg 12: @ laws of vector arithmetic;
pg 13: @ geometrical interpretation of abstract column vectors;
pg 14: @ A matrix as an array of numbers; scalar multiplication, addition, subtraction; matrices follow the same laws as vectors;
pg 15: @ define product of matrix and a column vector; define product of two 2by2 matrices;
pg 16: @ examples;
pg 17: @ determinants; alternate notation; theorem: determinant of product of matrices is equal to the product of the determinants of 2 matrices; exercises 5.1:2 ;
pg 18: @ exercises 5.3:5 ; THANKS to EmptySpace Enterprise
Introduction
Linear system of equations
Vector interpretation of a linear system
Change of coordinates
Matrix notation
Column vectors and matrices
Laws
Geometrical Interpretations
Matrices
Determinants
Insights into Mathematics
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