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Chapter 4: Matrices and Determinants (139 videos)
4.1: Introduction
  1. Introduction to Matrix
  2. More on Introducing Matrix
  3. Problem 1: Introduction to Matrix
4.2: Matrices
  1. More on Introducing Matrix DEMO
  2. Order of Matrix
  3. Problem 1: Order of Matrix
  4. Location of elements in Matrix
  5. Problem 1: Location of elements in Matrix
  6. Row Matrix and Column Matrix
  7. Problem 1: Row Matrix and Column Matrix
  8. Square Matrix and Rectangular Matrix
  9. Problem 1: Square Matrix and Rectangular Matrix
4.3: Notation
  1. Introduction to Matrix DEMO
  2. Problem 1: Introduction to Matrix
  3. Transpose of a Matrix
  4. Problem 1: Transpose of a Matrix
4.4: Special Types of Matrices
  1. Null Matrix or Zero Matrix DEMO
  2. Problem 1: Null Matrix or Zero Matrix
  3. Practical Application of Matrices
  4. Symmetric and Skew-Symmetric Matrices
  5. Problem 1: Symmetric and Skew-Symmetric Matrices
  6. Problem2-Symmetric & Skew-Symmetric Matrices
  7. Hermitian and Skew Hermitian Matrix
  8. Problem-Hermitian and Skew Hermitian Matrix
  9. Triangular Matrices
  10. Problem-Triangular Matrices
  11. Diagonal Matrix
  12. Problem 1: Diagonal Matrix
  13. Scalar Matrix
  14. Problem 1: Scalar Matrix
  15. Identity Matrix
  16. Problem 1: Identity Matrix
  17. Adjoint of a Matrix
  18. Problem 1: Adjoint of a Matrix
4.5: Algebra of Matrices
  1. Equal Matrices DEMO
  2. Problem 1: Equal Matrices
  3. Problem 2: Equal Matrices
  4. Addition of Matrices
  5. Problem 1: Addition of Matrices
  6. Subtraction of Matrices
  7. Problem 1: Subtraction of Matrices
  8. Multiplication of Matrix by a Real Number
  9. Problem 1: Multiplication of Matrix by a Real Number
  10. Multiplication of Matrices
  11. More on Multiplication of Matrices
  12. Problem 1: Multiplication of Matrices
  13. Problem 2: Multiplication of Matrices
  14. Problem3-Multiplication of Matrices
4.6: Properties of Matrix Operation
  1. Property for whole transpose of product of Matrices DEMO
  2. Property for Whole Inverse of Product of Matrices
  3. More on Property for Whole Inverse of Product of Matrices
  4. Problem 1: Property for whole transpose of product of Matrices
  5. Commutative Law under Addition for Matrices
  6. Problem 1: Commutative Law under Addition for Matrices
  7. Associaitve Law under Addition for Matrices
  8. Problem 1: Associaitve Law under Addition for Matrices
  9. Additive Identity of a Matrix
  10. Problem 1: Additive Identity of a Matrix
  11. Additive Inverse of a Matrix
  12. Problem 1: Additive Inverse of a Matrix
  13. Commutative Law of Multiplication of Matrices
  14. Problem 1: Commutative Law of Multiplication of Matrices
  15. Negative of Matrix
  16. Problem 1: Negative of Matrix
  17. Prove That c(AB) = (cA)B = A(cB)
  18. Problem-Prove That c(AB) = (cA)B = A(cB)
  19. Properties of Scalar Multiplication
  20. Associative law under Multiplication of matrices
  21. Problem 1: Associative law under Multiplication of matrices
  22. Distributive Law of Multiplication over Addition for Matrices
  23. Problem 1: Distributive Law of Multiplication over Addition for Matri
  24. Multiplicative Identity of a Matrix
  25. Problem 1: Multiplicative Identity of a Matrix
  26. Properties of Transposed Matrices
  27. Problem-Properties of Transposed Matrices
4.7: Determinant of a Square Matrix
  1. Determinant of 2-by-2 Matrix
  2. Problem1-Singular and Non-Singular Matrix
  3. Problem2-Singular and Non-Singular Matrix
4.8: Determinants of Order Two and Three
  1. Determinant of a Sqaure Matrix of Order 3 or greater
  2. Problem-Determinant of a Sqaure Matrix of Order 3 or greater
4.9: Properties of Determinants of Order Two
  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
4.10: Alternate Method For Expanding a Third Order Determinant
  1. Alternate Method For Expanding a Third Order Determinant
  2. Problem-Alternate Method For Expanding a Third Order Determinant
4.11: Properties of Determinants of Order Three
  1. Properties of Determinants of Order Three
  2. Problem-Properties of Determinants of Order Three
4.12: Minors and Cofactors of Elements of a Given Matrix A
  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. More on Matrix Inverse Using Adjoint
  6. Problem2-Matrix Inverse Using Adjoint
  7. Adjoint of a Square Matrix of Order n = 3 or n > 3
  8. Problem-Adjoint of a Square Matrix of Order n = 3 or n > 3
4.13: The Multiplicative Inverse of a Square Matrix
  1. Multiplicative Inverse of a Non-Singular Matrix DEMO
  2. Problem 1: Multiplicative Inverse of a Non-Singular Matrix
  3. Inverse of Matrix using Adjoint
  4. More on Matrix Inverse Using Adjoint
  5. Problem 1: Inverse of Matrix using Adjoint
  6. Problem2-Matrix Inverse Using Adjoint
  7. Problem3-Matrix Inverse Using Adjoint
  8. Problem4-Matrix Inverse Using Adjoint
  9. Adjoint of a Square Matrix of Order n = 3 or n > 3
  10. Problem-Adjoint of a Square Matrix of Order n = 3 or n > 3
  11. Deriving a Method For Determining Inverses
  12. Problem-Deriving a Method For Determining Inverses
  13. Inverse of Matrix by Row Operation
  14. Problem-Inverse of Matrix by Row Operation
  15. Problem-More on Inverse of Matrix by Row Operation
  16. Inverse of Matrix by Column Operation
  17. Problem-Inverse of Matrix by Column Operation
  18. Problem-More on Inverse of Matrix by Column Operation
  19. Echelon and Reduced Echelon Form of Matrix
  20. Problem-Echelon and Reduced Echelon Form of Matrix
  21. Echelon Form of Matrix
  22. Problem-Echelon Form of Matrix
  23. Reduced Echelon Form of Matrix
  24. Problem-Reduced Echelon Form of Matrix
  25. Rank of a Matrix
  26. Problem-Rank of a Matrix
  27. Invertible Matrix
  28. Problem-Invertible Matrix
  29. Theorems on Invertible Matrix
  30. More Theorems on Invertible Matrix
4.14: Distinction Between Homogeneous and Non-Homogeneous Systems of Linear Equations
  1. Solution of Homogeneous Linear Equations
  2. More on Solution of Homogeneous Linear Equations
  3. Problem-Solution of Homogeneous Linear Equations
  4. More on Problem-Solution of Homogeneous Linear Equations
4.15: olving a System of Three Non-Homogeneous Linear Equations in Three Unknowns
  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
 

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