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Change of Coordinates and Determinants - Wild Linear Algebra A
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- 1 CONTENT SUMMARY: pg 1: @ inverting the relationship between two pairs of variables;
- 2 pg 2: @ application of change of coordinates;
- 3 pg 3: @ changing coordinates is related to solving a system of linear equations; a family of problems
- 4 pg 4: @ example with parallel lines; zero determinant then 2 lines parallel 2-dim;
- 5 pg 5: @ Vector interpretation of a linear system;
- 6 pg 6: @ example of 2 vector system without solution;
- 7 pg 7: @ change of coordinants as heart of the subject;
- 8 pg 8: @ generalize the example on the previous page;
- 9 pg 9: @ matrix notation; a column vector; matrix/vector multiplication;
- 10 pg 10: @ writing a pair of linear equations in matrix/vector form;
- 11 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 multipl…
- 12 pg 12: @ laws of vector arithmetic;
- 13 pg 13: @ geometrical interpretation of abstract column vectors;
- 14 pg 14: @ A matrix as an array of numbers; scalar multiplication, addition, subtraction; matrices follow the same laws as vectors;
- 15 pg 15: @ define product of matrix and a column vector; define product of two 2by2 matrices;
- 16 pg 16: @ examples;
- 17 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 ;
- 18 pg 18: @ exercises 5.3:5 ; THANKS to EmptySpace Enterprise
- 19 Introduction
- 20 Linear system of equations
- 21 Vector interpretation of a linear system
- 22 Change of coordinates
- 23 Matrix notation
- 24 Column vectors and matrices
- 25 Laws
- 26 Geometrical Interpretations
- 27 Matrices
- 28 Determinants
