Some of the
main topics for Mathematics chapter Determinants(Class 12) along with
their details are:
1. Introduction to
Determinants:
(i)
Definition of Determinant, (ii) Order of Determinant, (iii) Elements of
Determinant, (iv) Properties of Determinants, (v) Evaluating Determinants
2. Types of
Determinants:
(i)
Scalar Determinant, (ii) Matrix Determinant, (iii) Minors and Cofactors, (iv)
Expansion of Determinants
3. Properties of
Determinants:
(i)
Square Matrix Property, (ii) Interchange of Rows Property, (iii) Interchange of
Columns Property,
(iv)
Multiplication of any Row or Column by a Constant Property,
(v) Sum
or Difference of Two Rows or Columns Property,
(vi)
Multiplication of Two Rows or Columns Property, (vii) Transpose of a Matrix
Property,
(viii)
Reciprocal of a Determinant Property
4. Adjoint and Inverse
of a Matrix:
(i)
Adjoint of a Matrix, (ii) Finding Adjoint using Cofactors, (iii) Inverse of a
Matrix,
(iv)
Finding Inverse using Adjoint and Determinant Property, (v) Criteria for
Existence of Inverse Matrix
5. Singular and
Non-singular Matrices:
(i)
Definition of Singular and Non-singular Matrix, (ii) Determinant of Singular
and Non-singular Matrix
6. Solution of Linear
Equations using Determinants:
(i)
Formulating Linear Equations using Determinants, (ii) Solving Linear Equations
using Inverse Matrix and Determinant
7. Applications of
Determinants:
(i) Area
and Volume of Figures, (ii) Solution of Simultaneous Linear Equations, (iii)
Cramer's Rule, (iv) Eigenvalues and Eigenvectors
8. Summary of Topics:
(i)
Recapitulation of concepts, (ii) Important Formulas for Matrices and
Determinants.
More Chapters:-
Main topics for Continuity and Differentiability
Main topics for Applications of Derivatives
click here for
other chapters.
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