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Chapter 3: Matrices and Determinants (158 videos)
3.1: Introduction
  1. Introduction to Matrix DEMO
  2. More on Introducing Matrix
  3. Problem 1: Introduction to Matrix
  4. Order of Matrix
  5. Problem 1: Order of Matrix
  6. Equal Matrices
  7. Problem 1: Equal Matrices
  8. Problem 2: Equal Matrices
  9. Row Matrix and Column Matrix
  10. Problem 1: Row Matrix and Column Matrix
  11. Square Matrix and Rectangular Matrix
  12. Problem 1: Square Matrix and Rectangular Matrix
  13. Null Matrix or Zero Matrix
  14. Problem 1: Null Matrix or Zero Matrix
  15. Practical Application of Matrices
  16. Transpose of a Matrix
  17. Problem 1: Transpose of a Matrix
  18. Negative of Matrix
  19. Problem 1: Negative of Matrix
  20. Symmetric and Skew-Symmetric Matrices
  21. Problem 1: Symmetric and Skew-Symmetric Matrices
  22. Problem2-Symmetric & Skew-Symmetric Matrices
  23. Hermitian and Skew Hermitian Matrix
  24. Problem-Hermitian and Skew Hermitian Matrix
  25. Triangular Matrices
  26. Problem-Triangular Matrices
  27. Diagonal Matrix
  28. Problem 1: Diagonal Matrix
  29. Scalar Matrix
  30. Problem 1: Scalar Matrix
  31. Identity Matrix
  32. Problem 1: Identity Matrix
  33. Adjoint of a Matrix
  34. Problem 1: Adjoint of a Matrix
  35. Addition of Matrices
  36. Problem 1: Addition of Matrices
  37. Subtraction of Matrices
  38. Problem 1: Subtraction of Matrices
  39. Multiplication of Matrix by a Real Number
  40. Problem 1: Multiplication of Matrix by a Real Number
  41. Multiplicative Identity of a Matrix
  42. Problem 1: Multiplicative Identity of a Matrix
  43. Properties of Transposed Matrices
  44. Problem-Properties of Transposed Matrices
  45. Multiplication of Matrices
  46. More on Multiplication of Matrices
  47. Problem 1: Multiplication of Matrices
  48. Problem 2: Multiplication of Matrices
  49. Problem3-Multiplication of Matrices
3.2: Determinant of a 2x2 Matrix
  1. Determinant of 2-by-2 Matrix DEMO
  2. Problem1-Singular and Non-Singular Matrix
  3. Problem2-Singular and Non-Singular Matrix
  4. Singular and Non-singular Matrix
  5. Problem 1: Singular and Non-singular Matrix
  6. Adjoint of a Matrix
  7. Problem 1: Adjoint of a Matrix
  8. Multiplicative Inverse of a Non-Singular Matrix
  9. Problem 1: Multiplicative Inverse of a Non-Singular Matrix
  10. Inverse of Matrix using Adjoint
  11. More on Matrix Inverse Using Adjoint
  12. Problem 1: Inverse of Matrix using Adjoint
  13. Problem2-Matrix Inverse Using Adjoint
  14. Problem3-Matrix Inverse Using Adjoint
  15. Problem4-Matrix Inverse Using Adjoint
3.3: Solution of Simultaneous Linear Equations By Using Matrices
  1. Solving Simultaneous Equations-Inversion Method
  2. Use of Matrices in Solving Everyday Life Problems
3.4: Field
  1. Introducing Field
  2. Problem-Introducing Field
3.5: Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplication
  1. Commutative Law under Addition for Matrices DEMO
  2. Problem 1: Commutative Law under Addition for Matrices
  3. Associaitve Law under Addition for Matrices
  4. Problem 1: Associaitve Law under Addition for Matrices
  5. Additive Identity of a Matrix
  6. Problem 1: Additive Identity of a Matrix
  7. Additive Inverse of a Matrix
  8. Problem 1: Additive Inverse of a Matrix
  9. Multiplication of Matrices
  10. Problem 1: Multiplication of Matrices
  11. Problem 2: Multiplication of Matrices
  12. Associative law under Multiplication of matrices
  13. Problem 1: Associative law under Multiplication of matrices
  14. Distributive Law of Multiplication over Addition for Matrices
  15. Problem 1: Distributive Law of Multiplication over Addition for Matri
  16. Commutative Law of Multiplication of Matrices
  17. Problem 1: Commutative Law of Multiplication of Matrices
  18. Prove That c(AB) = (cA)B = A(cB)
  19. Problem-Prove That c(AB) = (cA)B = A(cB)
  20. Properties of Scalar Multiplication
3.6: Determinants
  1. Minor of an Element of a Matrix or Its Determinant DEMO
  2. Problem-Minor of an Element of a Matrix or Its Determinant
  3. Cofactor of an Element of a Matrix
  4. Problem-Cofactor of an Element of a Matrix
  5. Determinant of a Sqaure Matrix of Order 3 or greater
  6. Problem-Determinant of a Sqaure Matrix of Order 3 or greater
3.7: Properties of Determinants Which Help in Their Evaluation
  1. Properties of Determinants DEMO
  2. More on Properties of Determinants
  3. Problem 1-Properties of Determinants
  4. Problem 2-Properties of Determinants
  5. Problem 3-Properties of Determinants
  6. Problem 4-Properties of Determinants
  7. Properties of Determinants of Order Three
  8. Problem-Properties of Determinants of Order Three
  9. Alternate Method For Expanding a Third Order Determinant
  10. Problem-Alternate Method For Expanding a Third Order Determinant
3.8: Adjoint and Inverse of a Square Matrix of Order n = 3 or n > 3
  1. Inverse of Matrix using Adjoint DEMO
  2. More on Matrix Inverse Using Adjoint
  3. Problem 1: Inverse of Matrix using Adjoint
  4. Problem2-Matrix Inverse Using Adjoint
  5. 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
  7. Property for whole transpose of product of Matrices
  8. Property for Whole Inverse of Product of Matrices
  9. More on Property for Whole Inverse of Product of Matrices
  10. Problem 1: Property for whole transpose of product of Matrices
3.9: Elementary Row and Column Operations on a Matrix
  1. Deriving a Method For Determining Inverses DEMO
  2. Problem-Deriving a Method For Determining Inverses
  3. Inverse of Matrix by Row Operation
  4. Problem-Inverse of Matrix by Row Operation
  5. Problem-More on Inverse of Matrix by Row Operation
  6. Inverse of Matrix by Column Operation
  7. Problem-Inverse of Matrix by Column Operation
  8. Problem-More on Inverse of Matrix by Column Operation
  9. Triangular Matrices
  10. Problem-Triangular Matrices
  11. Symmetric and Skew-Symmetric Matrices
  12. Problem 1: Symmetric and Skew-Symmetric Matrices
  13. Hermitian and Skew Hermitian Matrix
  14. Problem-Hermitian and Skew Hermitian Matrix
3.10: Echelon and Reduced Echelon Forms of Matrices
  1. Echelon and Reduced Echelon Form of Matrix DEMO
  2. Problem-Echelon and Reduced Echelon Form of Matrix
  3. Echelon Form of Matrix
  4. Problem-Echelon Form of Matrix
  5. Reduced Echelon Form of Matrix
  6. Problem-Reduced Echelon Form of Matrix
  7. Rank of a Matrix
  8. Problem-Rank of a Matrix
  9. Invertible Matrix
  10. Problem-Invertible Matrix
  11. Theorems on Invertible Matrix
  12. More Theorems on Invertible Matrix
3.11: Systems of Linear Equations
  1. Solution of System of Linear Equations by Row Operation DEMO
  2. Problem-Solution of System of Linear Equations by Row Operation
  3. Problem-More on Solution of System of Linear Equations by Row Operati
  4. Solution of Homogeneous Linear Equations
  5. More on Solution of Homogeneous Linear Equations
  6. Problem-Solution of Homogeneous Linear Equations
  7. More on Problem-Solution of Homogeneous Linear Equations
3.12: Cramer's Rule
  1. System of Linear Equations DEMO
  2. More on System of Linear Equations
  3. Problem-System of Linear Equations
  4. Consistency and Inconsistency of a System
  5. Problem-Consistency and Inconsistency of a System
  6. Solving a System of Three Non-Homogeneous Linear Equations
  7. Problem-Solving a System of Three Non-Homogeneous Linear Equations
  8. Solving Simultaneous Equations-Cramers Rule
  9. More on Use of Matrices Solving Everyday Life Problems
  10. More on Solving Simultaneous Equations-Cramers Rule
  11. Problem-Solving Simultaneous Equations-Cramers Rule
 

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