Topics
Relations and Functions
Relations and Functions
Algebra
Inverse Trigonometric Functions
Calculus
Matrices
- Concept of Matrices
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- Properties of Matrix Multiplication
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Invertible Matrices
- Overview of Matrices
- Negative of Matrix
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- Proof of the Uniqueness of Inverse
- Symmetric and Skew Symmetric Matrices
Determinants
- Determinants of Matrix of Order One and Two
- Determinant of a Matrix of Order 3 × 3
- Minors and Co-factors
- Inverse of a Square Matrix by the Adjoint Method
- Applications of Determinants and Matrices
- Symmetric and Skew Symmetric Matrices
- Properties of Determinants
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- Rule A=KB
- Overview of Determinants
- Geometric Interpretation of the Area of a Triangle
Vectors and Three-dimensional Geometry
Continuity and Differentiability
- Continuous and Discontinuous Functions
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- Mean Value Theorem
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Linear Programming
Applications of Derivatives
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
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Probability
Integrals
- Introduction of Integrals
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Sets
Applications of the Integrals
Differential Equations
- Differential Equations
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Vectors
- Vector
- Basic Concepts of Vector Algebra
- Direction Ratios, Direction Cosine & Direction Angles
- Vector Operations>Addition and Subtraction of Vectors
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- Vector Operations>Multiplication of a Vector by a Scalar
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- Introduction of Product of Two Vectors
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Three - Dimensional Geometry
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
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- Equation of a Line in Space
- Angle Between Two Lines
- Shortest Distance Between Two Lines
- Three - Dimensional Geometry Examples and Solutions
- Equation of a Plane Passing Through Three Non Collinear Points
- Equations of Line in Different Forms
- Coplanarity of Two Lines
- Distance of a Point from a Plane
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- Angle Between Two Planes
- Vector and Cartesian Equation of a Plane
- Equation of a Plane in Normal Form
- Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point
- Plane Passing Through the Intersection of Two Given Planes
- Overview of Three Dimensional Geometry
Linear Programming
Probability
Estimated time: 2 minutes
- Define symmetric and skew symmetric matrix
Maharashtra State Board: Class 12
Definition: Symmetric Matrix
A square matrix A = [aᵢⱼ]ₙ×ₙ is symmetric if Aᵀ = A
i.e., aᵢⱼ = aⱼᵢ for all i and j.
Maharashtra State Board: Class 12
Definition: Skew-Symmetric Matrix
Skew-Symmetric Matrix: A square matrix A = [aij] n×n is skew-symmetric if Aᵀ = −A i.e., aij = −aji for all i and j.
