Applications of 2x2 Matrices - Wild Linear Algebra A6

Applications of 2x2 Matrices - Wild Linear Algebra A6

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pg 10: @ writing a pair of linear equations in matrix/vector form;

10 of 27

10 of 27

pg 10: @ writing a pair of linear equations in matrix/vector form;

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Applications of 2x2 Matrices - Wild Linear Algebra A6

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

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