David J. Krus presents Matrix Algebra for Social Sciences

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David J. Krus presents Matrix Algebra for Social Sciences - PowerPoint PPT Presentation

David J. Krus presents Matrix Algebra for Social Sciences. Introduction to Matrix Algebra. Dimensions of a Matrix. Number of Rows: 2 Number of Columns:3 A 2 x 3 Matrix. Elements of a Matrix. Principal Diagonal Elements . Off-Diagonal Elements . Nomenclature of Matrices. Rectangular

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David J. Krus presents Matrix Algebra for Social Sciences

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1. David J. KruspresentsMatrix Algebrafor Social Sciences

2. Introduction toMatrix Algebra

3. Dimensions of a Matrix • Number of Rows: 2 • Number of Columns:3 • A 2 x 3 Matrix

4. Elements of a Matrix

5. Principal Diagonal Elements

6. Off-Diagonal Elements

7. Nomenclature of Matrices • Rectangular • Square • Symmetric • Skew Symmetric

8. Transpose

9. Triangulation

10. Matrix Algebra Operations on Matrix Elements

11. Addition of Matrix Elements • All matrices must have the the same dimensions. • The plus sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

13. Subtraction of Matrix Elements • All matrices must have the the same dimensions. • The subtraction sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

14. Subtraction of Matrix Elements

15. Multiplication of Matrix Elements • All matrices must have the the same dimensions. • The multiplication sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

16. Multiplication of Matrix Elements

17. Division of Matrix Elements • All matrices must have the the same dimensions or the divisor must be a scalar number. • The division sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

18. Division of Matrix Elements

19. Powers of Matrix Elements • The square sign is enclosed in parentheses.

20. Powers of Matrix Elements • The square sign is enclosed in parentheses

21. Matrix Algebra Operations on Matrices

22. Addition of Matrices 3 x 1 1 x 3 3 x 3

23. Major Addition of Matrices 1 + 1 = 2 1 + 2 = 3 1 + 3 = 4

24. Major Addition of Matrices 2 + 1 = 3 2 + 2 = 4 2 + 3 = 5

25. Major Addition of Matrices 3 + 1 = 4 3 + 2 = 5 3 + 3 = 6

26. Minor Addition of Matrices (1+1) + (2+2) + (3+3) = 12

27. Subtraction of Matrices 1 x 3 3 x 1 1 x 1

28. Minor Subtraction of Matrices (1-1) + (2-2) + (3-3) =0

29. Major Subtraction of Matrices 1 - 1 = 0 1 - 2 = -1 1 - 3 = -2

30. Major Subtraction of Matrices 2 - 1 = 1 2 - 2 = 0 2 - 3 = -1

31. Major Subtraction of Matrices 3 - 1 = 2 3 - 2 = 1 3 - 3 = 0

32. Multiplication of Matrices 3 x 2 2 x 3 3 x 3

33. Multiplication of Matrices (1*7) + (2*10) =27 (1*8) + (2*11) =30 (1*9) + (2*12) =33

34. Multiplication of Matrices (3*7) + (4*10) = 61 (3*8) + (4*11) = 68 (3*9) + (4*12) = 75

35. Multiplication of Matrices (5*7) + (6*10) = 95 (5*8) + (6*11) = 106 (5*9) + (6*12) = 117

36. Matrix Inversion

37. Matrix Inversion

38. Matrix Inversion

39. Powers of Matrices

40. Powers of Matrices (1*1) + (2*3) = 7 (1*2) + (2*4) = 10 (3*1) + (4*3) = 15 (3*2) + (4*4) = 22

41. Elements Of Statistics

42. Algebraic Mean In Summation Notation

43. Summation Notation

44. Algebraic Mean In Matrix Algebra Notation

45. Matrix Algebra Notation

46. Matrix Multiplication

47. Mean

48. True Variance In Summation Notation

49. Summation Notation

50. True Variance In Matrix Algebra Notation