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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
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
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
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
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
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
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
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
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
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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