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Table of contents

  • 1. Matrices | Order of a Matrix | Square and Rectangular Matrix
  • 2. Types of Matrices - Row - Column - Diagonal - Scalar - Identity Matrix
  • 3. Null and Equal Matrices
  • 4. Addition and Transpose of Matrices
  • 5. Example1 - Addition and Transpose of two matrices
  • 6. Subtraction and Multiplication of Matrices
  • 7. Example 2 - Multiplication of two similar and different matrices
  • 8. Determinant, Adjoint, Singular, Non Singular Matrices
  • 9. Inverse of matrices, Inverse of a 2x2 matrix
  • 10. Multiplication of matrices and subtraction of matrices
  • 11. Scalar Multiplication and subtraction of matrices
  • 12. Matrices - Scalar multiplication of matrices with examples (9, E3-1, Q5-6)
  • 13. Multiplication of matrices with examples (10, E3-1, Q8-9)
  • 14. Null and Equal Matrices (3)
  • 15. Transpose of Matrices | Addition | Multiplication of Matrices (22, E3.1, Q10-11)
  • 16. Matrices , Finding unknown from equal matrices (16, E3-1, Q3-4)
  • 17. Multiplication of same matrices, subtraction (14, E3-1, Q1-2)
  • 18. Multiplication of two scalars with a matrix (18, E3-1, Q 5-6)
  • 19. Finding unknown when product of a matrix by itself is null matrix (21, E3-1, Q8-9)
  • 20. Find unknown matrix by inverse method (23, E3-1, Q12i)
  • 21. Find unknown matrix A by inverse method (26, E3-1, Q-13ii)
  • 22. Proof of Multiplication of two matrices (27, Q-14)
  • 23. Definition of Field (28)
  • 24. Properties of matrix addition, scalar multiplication and matrix multiplication (29)
  • 25. Addition , Transpose , Multiplication of matrices with examples (22, E3-1, Q10-11, 1)
  • 26. Multiplication of identity and a matrix , Inverse of a matrix (32, E3-2, Q1-2)
  • 27. Solve the system of linear equations by matrices (34, E3-2, Q-3ii, 4ii)
  • 28. Proof for distributive property, Identities in matrices (36, E3-2, Q5ii, 6iii)
  • 29. Multiplication of a matrix and its transpose, Find unknown matrix (38, E3-2, Q7, 8i)
  • 30. Solution of matrix equation for unknown matrix (40, E3-2, Q9i)
  • 31. Determinants, Minor of an elements, Cofactor of an element (42)
  • 32. Properties of determinants, Matrices (44)
  • 33. Adjoint and inverse of a square matrix of order 3 (48)
  • 34. Evaluation of determinants with and without expansion (50, E3-3, Q1i, 2iii)
  • 35. Evaluation of determinants (51, E3-3, Q1iv)
  • 36. Applications of properties determinants (53, E3-3, Q3ii, 4i)
  • 37. Applications of properties of determinants (54, E3-3, 3iv)
  • 38. Applications of properties determinants (55, E3-3, Q3vii)
  • 39. Verify a determinant and find unknown variable (58, E3-3, Q5ii, 6ii)
  • 40. Verify determinants without expansion (59, E3-3, Q5vi)
  • 41. Evaluate determinants with examples (62, E3-3, Q7ii, 8)
  • 42. Application of property of transpose and order of a square (64, E3-3, Q9ii,10)
  • 43. Find value of unknown if given matrices are singular (66, E3-3, Q11, 12i)
  • 44. Inverse by using cofactors, Multiplication of matrix and its inverse (68, E3-3, Q13)
  • 45. Verify property of inverse and transpose (69, E3-3, Q14i, 15)
  • 46. Transpose and inverse of matrices (71, Q16, Q17ii)
  • 47. Triangular matrix, Upper triangular matrix, Lower triangular matrix (74)
  • 48. Symmetric matrices, skew symmetric matrices (75)
  • 49. Hermitian matrix and skew-Hermitian matrix (76)
  • 50. Echelon form of a matrix, Leading entry of a row in matrices (77)
  • 51. Reduced echelon form of a matrix, Rank of a matrix (78)
  • 52. Addition of matrices is symmetric (82, E3-4, Q1, 2i)
  • 53. Proof of addition and multiplication of symmetric matrices (84, E3-4, Q3i, 4)
  • 54. Hermitian matrix (86, E3-4, Q5, 6i)
  • 55. Application of Hermitian matrix, Proof of powers of a matrix (88, E3-4, Q7, 8)
  • 56. Inverse of matrices by using cofactors, row and column operation (89, E3-4, Q9i)
  • 57. Rank of matrices, Rank of a matrix (91, E3-4, Q10i)
  • 58. System of homogeneous and non homogeneous linear equations (93)
  • 59. Consistent and inconsistent, Trivial and non-trivial solution of homogeneous linear equations (95)
  • 60. Cramer’s rule, System of linear equations by Cramer’s rule (99, E3-5, Q1i)
  • 61. System of linear equations by inversion method, 100, Exercise 3-5, Question 2i
  • 62. System of equations by echelon and reduced echelon form, 102, Exercise 3.5, Question 3i
  • 63. Solution of system of homogeneous linear equations, 103, Exercise 3.5, Question 4i
  • 64. Find unknown value when systems have non trivial solutions, 105, Exercise 3 .5, Question 5i
  • 65. Find unknown value when system does not possess unique solution, 106, Exercise 3.5, Question 6

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System of equations by echelon and reduced echelon form, 102, Exercise 3.5, Question 3i

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