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Chapter 3: Matrices and Determinants (130 videos)  (Practice Test)
3.1: Definitions and Examples  (Practice Test)
  1. Introduction to Matrix
  2. More on Introducing Matrix
  3. Problem 1: Introduction to Matrix
  4. Order of Matrix
  5. Problem 1: Order of Matrix
  6. Location of elements in Matrix
  7. Problem 1: Location of elements in Matrix
  8. Equal Matrices
  9. Problem 1: Equal Matrices
  10. Problem 2: Equal Matrices
  11. Row Matrix and Column Matrix
  12. Problem 1: Row Matrix and Column Matrix
  13. Square Matrix and Rectangular Matrix
  14. Problem 1: Square Matrix and Rectangular Matrix
  15. Null Matrix or Zero Matrix
  16. Practical Application of Matrices
  17. Problem 1: Null Matrix or Zero Matrix
  18. Transpose of a Matrix
  19. Problem 1: Transpose of a Matrix
  20. Negative of Matrix
  21. Problem 1: Negative of Matrix
  22. Symmetric and Skew-Symmetric Matrices
  23. Problem 1: Symmetric and Skew-Symmetric Matrices
  24. Problem2-Symmetric & Skew-Symmetric Matrices
  25. Hermitian and Skew Hermitian Matrix
  26. Problem-Hermitian and Skew Hermitian Matrix
  27. Triangular Matrices
  28. Problem-Triangular Matrices
  29. Diagonal Matrix
  30. Problem 1: Diagonal Matrix
  31. Scalar Matrix
  32. Problem 1: Scalar Matrix
  33. Identity Matrix
  34. Problem 1: Identity Matrix
  35. Adjoint of a Matrix
  36. Problem 1: Adjoint of a Matrix
3.2: Algebraic Properties of Matrix Operations  (Practice Test)
  1. Multiplication of Matrices
  2. More on Multiplication of Matrices
  3. Problem 1: Multiplication of Matrices
  4. Problem 2: Multiplication of Matrices
  5. Problem3-Multiplication of Matrices
  6. Commutative Law under Addition for Matrices
  7. Problem 1: Commutative Law under Addition for Matrices
  8. Associaitve Law under Addition for Matrices
  9. Problem 1: Associaitve Law under Addition for Matrices
  10. Additive Identity of a Matrix
  11. Problem 1: Additive Identity of a Matrix
  12. Additive Inverse of a Matrix
  13. Problem 1: Additive Inverse of a Matrix
  14. Commutative Law of Multiplication of Matrices
  15. Problem 1: Commutative Law of Multiplication of Matrices
  16. Properties of Scalar Multiplication
  17. Prove That c(AB) = (cA)B = A(cB)
  18. Problem-Prove That c(AB) = (cA)B = A(cB)
  19. Associative law under Multiplication of matrices
  20. Problem 1: Associative law under Multiplication of matrices
  21. Distributive Law of Multiplication over Addition for Matrices
  22. Problem 1: Distributive Law of Multiplication over Addition for Matri
  23. Multiplicative Identity of a Matrix
  24. Problem 1: Multiplicative Identity of a Matrix
  25. Properties of Transposed Matrices
  26. Problem-Properties of Transposed Matrices
  27. Property for whole transpose of product of Matrices
  28. Property for Whole Inverse of Product of Matrices
  29. More on Property for Whole Inverse of Product of Matrices
  30. Problem 1: Property for whole transpose of product of Matrices
  31. Introducing Field
  32. Problem-Introducing Field
3.3: Elementary Row and Column Operations on a Matrix  (Practice Test)
  1. Deriving a Method For Determining Inverses
  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
3.4: Echelon Form of Matrix  (Practice Test)
  1. Echelon and Reduced Echelon Form of Matrix
  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
3.5: Rank and Inverse of a Matrix  (Practice Test)
  1. Multiplicative Inverse of a Non-Singular Matrix
  2. Problem 1: Multiplicative Inverse of a Non-Singular Matrix
  3. Inverse of Matrix using Adjoint
  4. Problem 1: Inverse of Matrix using Adjoint
  5. Rank of a Matrix
  6. Problem-Rank of a Matrix
  7. Invertible Matrix
  8. Problem-Invertible Matrix
  9. Theorems on Invertible Matrix
  10. More Theorems on Invertible Matrix
3.6: Minors and Cofactors  (Practice Test)
  1. Minor of an Element of a Matrix or Its Determinant
  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
3.7: Properties of Determinants  (Practice Test)
  1. Properties of Determinants
  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
3.8: Adjoint and Inverse of a Matrix   (Practice Test)
  1. Inverse of Matrix using Adjoint
  2. More on Matrix Inverse Using Adjoint
  3. Problem 1: Inverse of Matrix using Adjoint
  4. Problem2-Matrix Inverse Using Adjoint
  5. Problem3-Matrix Inverse Using Adjoint
  6. Problem4-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
3.9: Homogeneous Systems of Linear Equations  (Practice Test)
  1. System of Linear Equations
  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
3.10: Non-Homogeneous Systems of Linear Equations  (Practice Test)
  1. Solving a System of Three Non-Homogeneous Linear Equations
  2. Problem-Solving a System of Three Non-Homogeneous Linear Equations
  3. Solution of Homogeneous Linear Equations
  4. More on Solution of Homogeneous Linear Equations
  5. Problem-Solution of Homogeneous Linear Equations
  6. More on Problem-Solution of Homogeneous Linear Equations
  7. Solution of System of Linear Equations by Row Operation
  8. Problem-Solution of System of Linear Equations by Row Operation
  9. Problem-More on Solution of System of Linear Equations by Row Operati
  10. Solving Simultaneous Equations-Inversion Method
  11. More on Solving Simultaneous Equations-Inversion Method
  12. Use of Matrices in Solving Everyday Life Problems
3.11: Cramer's Rule
  1. More on Solving Simultaneous Equations-Cramers Rule
  2. More on Use of Matrices Solving Everyday Life Problems
  3. Problem-Solving Simultaneous Equations-Cramers Rule
 

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