Topics
Relations and Functions
Relations and Functions
Inverse Trigonometric Functions
- Meaning and Interpretation of Inverse Trigonometric Functions
- Inverse Trigonometric Functions (Simplification and Examples)
- Properties of Inverse Trigonometric Functions
- Graphs and Domains & Ranges of Inverse Trigonometric Functions
- Principal Values of Inverse Trigonometric Functions
- Overview of Inverse Trigonometric Functions
Algebra
Calculus
Matrices
- Concept of Matrices
- Types of Matrices
- Equality of Matrices
- Operation on Matrices
- Multiplication of a Matrix by a Scalar
- Properties of Matrix Addition
- Properties of Matrix Multiplication
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Invertible Matrices
- Overview of Matrices
- Negative of Matrix
- Operation on Matrices
- Proof of the Uniqueness of Inverse
- Symmetric and Skew Symmetric Matrices
Vectors and Three-dimensional Geometry
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
- Determinant of a Square Matrix
- Rule A=KB
- Overview of Determinants
- Geometric Interpretation of the Area of a Triangle
Linear Programming
Continuity and Differentiability
- Continuous and Discontinuous Functions
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivative of Composite Functions
- Derivatives of Implicit Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Derivative - Exponential and Log
- Proof Derivative X^n Sin Cos Tan
- Infinite Series
- Higher Order Derivative
- Mean Value Theorem
- Overview of Continuity and Differentiability
Applications of Derivatives
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
- Increasing and Decreasing Functions
- Maxima and Minima
- Maximum and Minimum Values of a Function in a Closed Interval
- Simple Problems on Applications of Derivatives
- Graph of Maxima and Minima
- Approximations
- Tangents and Normals
- Overview of Applications of Derivatives
Probability
Sets
Integrals
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
- Some Properties of Indefinite Integral
- Methods of Integration> Integration by Substitution
- Integration Using Trigonometric Identities
- Integrals of Some Particular Functions
- Methods of Integration> Integration Using Partial Fraction
- Methods of Integration> Integration by Parts
- Fundamental Theorem of Integral Calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
- Definite Integrals
- Indefinite Integral Problems
- Comparison Between Differentiation and Integration
- Geometrical Interpretation of Indefinite Integrals
- Indefinite Integral by Inspection
- Definite Integral as the Limit of a Sum
- Evaluation of Simple Integrals of the Following Types and Problems
- Overview of Integrals
Applications of the Integrals
Differential Equations
- Differential Equations
- Order and Degree of a Differential Equation
- General and Particular Solutions of a Differential Equation
- Linear Differential Equations
- Homogeneous Differential Equations
- Solutions of Linear Differential Equation
- Equations in Variable Separable Form
- Formation of a Differential Equation Whose General Solution is Given
- Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
- Overview of Differential Equations
Vectors
- Vector
- Basic Concepts of Vector Algebra
- Direction Ratios, Direction Cosine & Direction Angles
- Vector Operations>Addition and Subtraction of Vectors
- Properties of Vector Addition
- Vector Operations>Multiplication of a Vector by a Scalar
- Components of Vector
- Vector Joining Two Points
- Section Formula
- Vector (Or Cross) Product of Two Vectors
- Scalar (Or Dot) Product of Two Vectors
- Projection of a Vector on a Line
- Geometrical Interpretation of Scalar
- Scalar Triple Product
- Position Vector of a Point Dividing a Line Segment in a Given Ratio
- Magnitude and Direction of a Vector
- Vectors Examples and Solutions
- Introduction of Product of Two Vectors
- Overview of Vectors
Three - Dimensional Geometry
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
- Relation Between Direction Ratio and Direction Cosines
- 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
- Angle Between Line and a Plane
- 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
- Matrices
- Determinants
- Cramer’s Rule
- Application in Economics
CISCE: Class 10
Definition: Matrix
A matrix is a rectangular arrangement of numbers arranged in rows and columns, enclosed in brackets [ ] or parentheses ( ).
Elements (Entries) of a Matrix
- Each number in a matrix is called an element (or entry).
Rows and Columns
- Horizontal lines → rows
- Vertical lines → columns
Order of a Matrix
- Order = number of rows × number of columns
- Written as m × n and read as “m by n”
Video Tutorials
Shaalaa.com | Matrices Example 1
to track your progress
Series:
0%
Matrices Example 1
00:04:05 undefined
00:04:05 undefined
Matrices Example 2
00:04:43 undefined
00:04:43 undefined
Matrices Example 3
00:07:56 undefined
00:07:56 undefined
Matrices Example 4
00:04:18 undefined
00:04:18 undefined
Matrices Example 5
00:04:46 undefined
00:04:46 undefined
Matrices Example 6
00:04:24 undefined
00:04:24 undefined
Matrices Example 7
00:04:56 undefined
00:04:56 undefined
Matrices Example 8
00:08:16 undefined
00:08:16 undefined
Matrices Example 9
00:05:51 undefined
00:05:51 undefined
Matrices Example 10
00:05:28 undefined
00:05:28 undefined
Matrices Example 11
00:06:21 undefined
00:06:21 undefined
Matrices Example 12
00:07:55 undefined
00:07:55 undefined
Matrices Example 13
00:04:02 undefined
00:04:02 undefined
Matrices Example 14
00:03:57 undefined
00:03:57 undefined
