Matrices and Determinants

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    Chapter 3: Matrices and Determinants (157 videos)   (Practice Test)

      3.1: Introduction (Practice Test)
      Introducing Matrix
    1. Introducing Matrix
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      2. More on Introducing Matrix
    2. More on Introducing Matrix
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      3. Problem-Introducing Matrix
    3. Problem-Introducing Matrix
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      4. Order of Matrix
    4. Order of Matrix
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      5. Problem-Order of Matrix
    5. Problem-Order of Matrix
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      6. Equal Matrices
    6. Equal Matrices
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      7. Problem1-Equal Matrices
    7. Problem1-Equal Matrices
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      8. Problem2-Equal Matrices
    8. Problem2-Equal Matrices
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      9. Row-Column Matrix
    9. Row-Column Matrix
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      10. Problem-Row-Column Matrix
    10. Problem-Row-Column Matrix
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      11. Square-Rectangular Matrix
    11. Square-Rectangular Matrix
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      12. Problem-Square-Rectangular Matrix
    12. Problem-Square-Rectangular Matrix
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      13. Null Matrix or Zero Matrix
    13. Null Matrix or Zero Matrix
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      14. Problem-Null Matrix or Zero Matrix
    14. Problem-Null Matrix or Zero Matrix
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      15. Practical Application of Matrices
    15. Practical Application of Matrices
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      16. Transpose of Matrix
    16. Transpose of Matrix
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      17. Problem-Transpose of Matrix
    17. Problem-Transpose of Matrix
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      18. Negative of Matrix
    18. Negative of Matrix
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      19. Problem-Negative of Matrix
    19. Problem-Negative of Matrix
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      20. Symmetric & Skew-Symmetric Matrices
    20. Symmetric & Skew-Symmetric Matrices
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      21. Problem1-Symmetric & Skew-Symmetric Matrices
    21. Problem1-Symmetric & Skew-Symmetric Matrices
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      22. Problem2-Symmetric & Skew-Symmetric Matrices
    22. Problem2-Symmetric & Skew-Symmetric Matrices
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      23. Hermitian and Skew Hermitian Matrix
    23. Hermitian and Skew Hermitian Matrix
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      24. Problem-Hermitian and Skew Hermitian Matrix
    24. Problem-Hermitian and Skew Hermitian Matrix
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      25. Triangular Matrices
    25. Triangular Matrices
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      26. Problem-Triangular Matrices
    26. Problem-Triangular Matrices
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      27. Diagonal Matrix
    27. Diagonal Matrix
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      28. Problem-Diagonal Matrix
    28. Problem-Diagonal Matrix
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      29. Scalar Matrix
    29. Scalar Matrix
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      30. Problem-Scalar Matrix
    30. Problem-Scalar Matrix
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      31. Identity Matrix
    31. Identity Matrix
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      32. Problem-Identity Matrix
    32. Problem-Identity Matrix
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      33. Adjoint of Matrix
    33. Adjoint of Matrix
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      34. Problem-Adjoint of Matrix
    34. Problem-Adjoint of Matrix
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      35. Addition of Matrices
    35. Addition of Matrices
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      36. Problem-Addition of Matrices
    36. Problem-Addition of Matrices
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      37. Subtraction of Matrices
    37. Subtraction of Matrices
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      38. Problem-Subtraction of Matrices
    38. Problem-Subtraction of Matrices
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      39. Multiplication of Matrix by Real Number
    39. Multiplication of Matrix by Real Number
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      40. Problem-Multiplication of Matrix by Real Number
    40. Problem-Multiplication of Matrix by Real Number
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      41. Multiplicative Identity of a Matrix
    41. Multiplicative Identity of a Matrix
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      42. Problem-Multiplicative Identity of a Matrix
    42. Problem-Multiplicative Identity of a Matrix
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      43. Properties of Transposed Matrices
    43. Properties of Transposed Matrices
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      44. Problem-Properties of Transposed Matrices
    44. Problem-Properties of Transposed Matrices
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      45. Multiplication of Matrices
    45. Multiplication of Matrices
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      46. More on Multiplication of Matrices
    46. More on Multiplication of Matrices
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      47. Problem1-Multiplication of Matrices
    47. Problem1-Multiplication of Matrices
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      48. Problem2-Multiplication of Matrices
    48. Problem2-Multiplication of Matrices
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      49. Problem3-Multiplication of Matrices
    49. Problem3-Multiplication of Matrices
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      3.2: Determinant of a 2x2 Matrix (Practice Test)
      Determinant of 2-by-2 Matrix
    1. Determinant of 2-by-2 Matrix
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      2. Problem1-Singular and Non-Singular Matrix
    2. Problem1-Singular and Non-Singular Matrix
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      3. Problem2-Singular and Non-Singular Matrix
    3. Problem2-Singular and Non-Singular Matrix
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      4. Singular and Non-Singular Matrix
    4. Singular and Non-Singular Matrix
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      5. Problem-Singular and Non-Singular Matrix
    5. Problem-Singular and Non-Singular Matrix
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      6. Adjoint of Matrix
    6. Adjoint of Matrix
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      7. Problem-Adjoint of Matrix
    7. Problem-Adjoint of Matrix
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      8. Multiplicative Inverse of Non-Singular Matrix
    8. Multiplicative Inverse of Non-Singular Matrix
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      9. Problem-Multiplicative Inverse of Non-Singular Matrix
    9. Problem-Multiplicative Inverse of Non-Singular Matrix
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      10. Matrix Inverse Using Adjoint
    10. Matrix Inverse Using Adjoint
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      11. More on Matrix Inverse Using Adjoint
    11. More on Matrix Inverse Using Adjoint
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      12. Problem1-Matrix Inverse Using Adjoint
    12. Problem1-Matrix Inverse Using Adjoint
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      13. Problem2-Matrix Inverse Using Adjoint
    13. Problem2-Matrix Inverse Using Adjoint
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      14. Problem3-Matrix Inverse Using Adjoint
    14. Problem3-Matrix Inverse Using Adjoint
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      15. Problem4-Matrix Inverse Using Adjoint
    15. Problem4-Matrix Inverse Using Adjoint
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      3.3: Solution of Simultaneous Linear Equations By Using Matrices
      Solving Simultaneous Equations-Inversion Method
    1. Solving Simultaneous Equations-Inversion Method
      10163 views
      2. Problem-Solving Simultaneous Equations-Inversion Method
    2. Problem-Solving Simultaneous Equations-Inversion Method
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      3.4: Field
      Introducing Field
    1. Introducing Field
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      2. Problem-Introducing Field
    2. Problem-Introducing Field
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      3.5: Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplication (Practice Test)
      Commutative Law Under Addition for Matrices
    1. Commutative Law Under Addition for Matrices
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      2. Problem-Commutative Law Under Addition for Matrices
    2. Problem-Commutative Law Under Addition for Matrices
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      3. Associative Law under Addition and Multiplication of Matrices
    3. Associative Law under Addition and Multiplication of Matrices
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      4. Problem-Associative Law Under Addition for Matrices
    4. Problem-Associative Law Under Addition for Matrices
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      5. Additive Identity of a Matrix
    5. Additive Identity of a Matrix
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      6. Problem-Additive Identity of a Matrix
    6. Problem-Additive Identity of a Matrix
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      7. Additive Inverse of a Matrix
    7. Additive Inverse of a Matrix
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      8. Problem-Additive Inverse of a Matrix
    8. Problem-Additive Inverse of a Matrix
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      9. Multiplication of Matrices
    9. Multiplication of Matrices
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      10. Problem1-Multiplication of Matrices
    10. Problem1-Multiplication of Matrices
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      11. Problem2-Multiplication of Matrices
    11. Problem2-Multiplication of Matrices
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      12. Associative Law under Multiplication of Matrices
    12. Associative Law under Multiplication of Matrices
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      13. Problem-Associative Law under Multiplication of Matrices
    13. Problem-Associative Law under Multiplication of Matrices
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      14. Distributive Law of Matrices
    14. Distributive Law of Matrices
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      15. Problem-Distributivity of Matrices
    15. Problem-Distributivity of Matrices
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      16. Commutative Law of Multiplication of Matrices
    16. Commutative Law of Multiplication of Matrices
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      17. Problem-Commutative Law of Multiplication of Matrices
    17. Problem-Commutative Law of Multiplication of Matrices
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      18. Prove That c(AB) = (cA)B = A(cB)
    18. Prove That c(AB) = (cA)B = A(cB)
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      19. Problem-Prove That c(AB) = (cA)B = A(cB)
    19. Problem-Prove That c(AB) = (cA)B = A(cB)
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      20. Properties of Scalar Multiplication
    20. Properties of Scalar Multiplication
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      3.6: Determinants (Practice Test)
      Minor of an Element of a Matrix and Its Determinant
    1. Minor of an Element of a Matrix and Its Determinant
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      2. Problem-Minor of an Element of a Matrix or Its Determinant
    2. Problem-Minor of an Element of a Matrix or Its Determinant
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      3. Cofactor of an Element of a Matrix
    3. Cofactor of an Element of a Matrix
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      4. Problem-Cofactor of an Element of a Matrix
    4. Problem-Cofactor of an Element of a Matrix
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      5. Determinant of a Sqaure Matrix of Order 3 or greater
    5. Determinant of a Sqaure Matrix of Order 3 or greater
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      6. Problem-Determinant of a Sqaure Matrix of Order 3 or greater
    6. Problem-Determinant of a Sqaure Matrix of Order 3 or greater
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      3.7: Properties of Determinants Which Help in Their Evaluation (Practice Test)
      Properties of Determinants
    1. Properties of Determinants
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      2. More on Properties of Determinants
    2. More on Properties of Determinants
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      3. Problem 1-Properties of Determinants
    3. Problem 1-Properties of Determinants
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      4. Problem 2-Properties of Determinants
    4. Problem 2-Properties of Determinants
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      5. Problem 3-Properties of Determinants
    5. Problem 3-Properties of Determinants
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      6. Problem 4-Properties of Determinants
    6. Problem 4-Properties of Determinants
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      7. Properties of Determinants of Order Three
    7. Properties of Determinants of Order Three
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      8. Problem-Properties of Determinants of Order Three
    8. Problem-Properties of Determinants of Order Three
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      9. Alternate Method For Expanding a Third Order Determinant
    9. Alternate Method For Expanding a Third Order Determinant
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      10. Problem-Alternate Method For Expanding a Third Order Determinant
    10. Problem-Alternate Method For Expanding a Third Order Determinant
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      3.8: Adjoint and Inverse of a Square Matrix of Order n = 3 or n > 3 (Practice Test)
      Matrix Inverse Using Adjoint
    1. Matrix Inverse Using Adjoint
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      2. More on Matrix Inverse Using Adjoint
    2. More on Matrix Inverse Using Adjoint
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      3. Problem1-Matrix Inverse Using Adjoint
    3. Problem1-Matrix Inverse Using Adjoint
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      4. Problem2-Matrix Inverse Using Adjoint
    4. Problem2-Matrix Inverse Using Adjoint
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      5. Adjoint of a Square Matrix of Order n = 3 or n > 3
    5. Adjoint of a Square Matrix of Order n = 3 or n > 3
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      6. Problem-Adjoint of a Square Matrix of Order n = 3 or n > 3
    6. Problem-Adjoint of a Square Matrix of Order n = 3 or n > 3
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      7. Transpose of Product of Matrices
    7. Transpose of Product of Matrices
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      8. Property for Whole Inverse of Product of Matrices
    8. Property for Whole Inverse of Product of Matrices
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      9. More on Property for Whole Inverse of Product of Matrices
    9. More on Property for Whole Inverse of Product of Matrices
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      10. Problem- Matrices Law for Whole Transpose of Product
    10. Problem- Matrices Law for Whole Transpose of Product
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      3.9: Elementary Row and Column Operations on a Matrix (Practice Test)
      Deriving a Method For Determining Inverses
    1. Deriving a Method For Determining Inverses
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      2. Problem-Deriving a Method For Determining Inverses
    2. Problem-Deriving a Method For Determining Inverses
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      3. Inverse of Matrix by Row Operation
    3. Inverse of Matrix by Row Operation
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      4. Problem-Inverse of Matrix by Row Operation
    4. Problem-Inverse of Matrix by Row Operation
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      5. More on Problem- Inverse of Matrix by Row Operation
    5. More on Problem- Inverse of Matrix by Row Operation
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      6. Inverse of Matrix by Column Operation
    6. Inverse of Matrix by Column Operation
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      7. Problem-Inverse of Matrix by Column Operation
    7. Problem-Inverse of Matrix by Column Operation
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      8. More on Problem-Inverse of Matrix by Column Operation
    8. More on Problem-Inverse of Matrix by Column Operation
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      9. Triangular Matrices
    9. Triangular Matrices
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      10. Problem-Triangular Matrices
    10. Problem-Triangular Matrices
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      11. Symmetric & Skew-Symmetric Matrices
    11. Symmetric & Skew-Symmetric Matrices
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      12. Problem1-Symmetric & Skew-Symmetric Matrices
    12. Problem1-Symmetric & Skew-Symmetric Matrices
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      13. Hermitian and Skew Hermitian Matrix
    13. Hermitian and Skew Hermitian Matrix
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      14. Problem-Hermitian and Skew Hermitian Matrix
    14. Problem-Hermitian and Skew Hermitian Matrix
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      3.10: Echelon and Reduced Echelon Forms of Matrices (Practice Test)
      Echelon and Reduced Echelon Form of Matrix
    1. Echelon and Reduced Echelon Form of Matrix
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      2. Problem-Echelon and Reduced Echelon Form of Matrix
    2. Problem-Echelon and Reduced Echelon Form of Matrix
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      3. Echelon Form of Matrix
    3. Echelon Form of Matrix
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      4. Problem-Echelon Form of Matrix
    4. Problem-Echelon Form of Matrix
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      5. Reduced Echelon Form of Matrix
    5. Reduced Echelon Form of Matrix
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      6. Problem-Reduced Echelon Form of Matrix
    6. Problem-Reduced Echelon Form of Matrix
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      7. Rank of a Matrix
    7. Rank of a Matrix
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      8. Problem-Rank of a Matrix
    8. Problem-Rank of a Matrix
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      9. Invertible Matrix
    9. Invertible Matrix
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      10. Problem-Invertible Matrix
    10. Problem-Invertible Matrix
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      11. Theorems on Invertible Matrix
    11. Theorems on Invertible Matrix
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      12. More Theorems on Invertible Matrix
    12. More Theorems on Invertible Matrix
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      3.11: Systems of Linear Equations (Practice Test)
      Solution of System of Linear Equations by Row Operation
    1. Solution of System of Linear Equations by Row Operation
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      2. Problem-Solution of System of Linear Equations by Row Operation
    2. Problem-Solution of System of Linear Equations by Row Operation
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      3. Problem-More on Solution of System of Linear Equations by Row Operation
    3. Problem-More on Solution of System of Linear Equations by Row Operati
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      4. Solution of Homogeneous Linear Equations
    4. Solution of Homogeneous Linear Equations
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      5. More on Solution of Homogeneous Linear Equations
    5. More on Solution of Homogeneous Linear Equations
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      6. Problem-Solution of Homogeneous Linear Equations
    6. Problem-Solution of Homogeneous Linear Equations
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      7. More on Problem-Solution of Homogeneous Linear Equations
    7. More on Problem-Solution of Homogeneous Linear Equations
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      3.12: Cramer's Rule (Practice Test)
      System of Linear Equations
    1. System of Linear Equations
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      2. More on System of Linear Equations
    2. More on System of Linear Equations
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      3. Problem-System of Linear Equations
    3. Problem-System of Linear Equations
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      4. Consistency and Inconsistency of a System
    4. Consistency and Inconsistency of a System
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      5. Problem-Consistency and Inconsistency of a System
    5. Problem-Consistency and Inconsistency of a System
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      6. Solving a System of Three Non-Homogeneous Linear Equations
    6. Solving a System of Three Non-Homogeneous Linear Equations
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      7. Problem-Solving a System of Three Non-Homogeneous Linear Equations
    7. Problem-Solving a System of Three Non-Homogeneous Linear Equations
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      8. Solving Simultaneous Equations-Cramers Rule
    8. Solving Simultaneous Equations-Cramers Rule
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      9. Problem1-Solving Simultaneous Equations-Cramers Rule
    9. Problem1-Solving Simultaneous Equations-Cramers Rule
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      10. Problem2-Solving Simultaneous Equations-Cramers Rule
    10. Problem2-Solving Simultaneous Equations-Cramers Rule
      406 views