Introduction of Matrices

Topics

Mathematical Logic
- Statements - Introduction in Logic
- Logical Connective, Simple and Compound Statements
- Statement Patterns and Logical Equivalence
- Algebra of Statements
- Venn Diagrams
Mathematical Logic
- Truth Value of Statement
- Logical Connective, Simple and Compound Statements
- Quantifier and Quantified Statements in Logic
- Statement Patterns and Logical Equivalence
- Algebra of Statements
- Venn Diagrams
Matrices
- Determinant of a Matrix
- Types of Matrices
- Algebra of Matrices
- Properties of Matrices
- Elementary Transformations
- Inverse of Matrix
- Application of Matrices
Differentiation
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative
Applications of Derivatives
- Introduction of Derivatives
- Increasing and Decreasing Functions
- Maxima and Minima
- Application of Derivatives to Economics
Integration
- Integration
- Methods of Integration: Integration by Substitution
- Methods of Integration: Integration by Parts
- Methods of Integration: Integration Using Partial Fractions
Definite Integration
- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals
Applications of Definite Integration
- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves
Differential Equation and Applications
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations
Matrices
- Introduction of Matrices
- Algebra of Matrices
- Inverse of Matrix
- Solution of Equations
Commission, Brokerage and Discount
- Commission and Brokerage Agent
- Discount
Insurance and Annuity
- Concept of Insurance
- Fire Insurance
- Accident Insurance
- Marine Insurance
- Annuity
Linear Regression
- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
Time Series
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend
Index Numbers
- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem
Assignment Problem and Sequencing
- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence
Probability Distributions
- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
Continuity
- Continuous Function of Point
Differentiation
- Derivatives of Implicit Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Derivative of Inverse Function
Applications of Derivative
- Increasing and Decreasing Functions
- Maxima and Minima
Indefinite Integration
- Definition of an Integral
- Integral of Standard Functions
- Rules of Integration
- Methods of Integration
- Integration by Parts
Definite Integrals
- Properties of Definite Integrals
- Applications of Definite Integrals
Ratio, Proportion and Partnership
- Ratio, Proportion and Partnership
Commission, Brokerage and Discount
- Commission, Brokerage and Discount
Insurance and Annuity
- Insurance and Annuity
Demography
- Concept of Demography
- Uses of Vital Statistics in Demography
- Measurements of Mortality
- Life Tables
Bivariate Data and Correlation
- Bivariate Frequency Distribution
- Karl Pearson’s Coefficient of Correlation
- Rank Correlation
Regression Analysis Introduction
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Regression Coefficient of X on Y and Y on X
- Regression Propertise
Random Variable and Probability Distribution
- Random Variables and Its Probability Distributions
- Binomial Theorem and Binomial Distribution
- Poisson Distribution
- Normal Distribution
- Probability Distribution of a Discrete Random Variable
- Distribution Function of a Continuous Random Variable
Management Mathematics
- Inequations in Management Mathematics
- Linear Programming Problem in Management Mathematics
- Assignment Problem
- Sequencing in Management Mathematics

Matrices
Determinants
Cramer’s Rule
Application in Economics

Notes

A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix. We denote matrices by capital letters. The following are some examples of matrices:
A =`[(-2,5),(0, sqrt 5) , (3,6)] , B = [(2+i,3 , -1/2),(3.5,-1,2),(sqrt3 , 5 , 5/7)] , C = [(1+x , x^3,3),(cos x , sin x + 2 , tan x)]`
In the above examples, the horizontal lines of elements are said to constitute, rows of the matrix and the vertical lines of elements are said to constitute, columns of the matrix. Thus A has 3 rows and 2 columns, B has 3 rows and 3 columns while C has 2 rows and 3 columns.
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Introduction of Matrices

Topics

Mathematical Logic

Mathematical Logic

Matrices

Differentiation

Applications of Derivatives

Integration

Definite Integration

Applications of Definite Integration

Differential Equation and Applications

Matrices

Commission, Brokerage and Discount

Insurance and Annuity

Linear Regression

Time Series

Index Numbers

Linear Programming

Assignment Problem and Sequencing

Probability Distributions

Continuity

Differentiation

Applications of Derivative

Indefinite Integration

Definite Integrals

Ratio, Proportion and Partnership

Commission, Brokerage and Discount

Insurance and Annuity

Demography

Bivariate Data and Correlation

Regression Analysis Introduction

Random Variable and Probability Distribution

Management Mathematics

Notes

Video Tutorials

Shaalaa.com | Types Of Matrices

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