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David J. Krus presents Matrix Algebra for Social Sciences

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

  12. Addition of Matrix Elements

  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

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