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Introduction
forms the set of real numbers (ii..
forms the set of real numbers (ii..Summary
If x and y are any real numbers, then x+iy is called a complex number. In the complex number x+iy, the real numbers x and y are respectively called the real part and imaginary part of x+iy. Two complex numbers are s..
If x and y are any real numbers, then x+iy is called a complex number. In the complex number x+iy, the real numbers x and y are respectively called the real part and imaginary part of x+iy. Two complex numbers are s..Some important results
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This p..
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This p..Summary
A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be compa..
Definition
Let R i denotes the i t h row of the matrix A = [a i j ] then the elementary row operations on the matrix A are defined as: 3. R i g R i + kR j means multiply each element of j t h row by k and add it to the corresponding elements of i t h row. The corresponding column tra..
Let R i denotes the i t h row of the matrix A = [a i j ] then the elementary row operations on the matrix A are defined as: 3. R i g R i + kR j means multiply each element of j t h row by k and add it to the corresponding elements of i t h row. The corresponding column tra..Definition:
Union of two sets A and B is the set of all elements which are in A, or in B, or both in A and B. In Set builder form,..
Union of two sets A and B is the set of all elements which are in A, or in B, or both in A and B. In Set builder form,..Definition:
If A and B are any two sets then the relative complement of B in A is the set of all elements in A which are not in B. It is denoted by A - B..
If A and B are any two sets then the relative complement of B in A is the set of all elements in A which are not in B. It is denoted by A - B..Definition of ratio
Definition of ratio - If a and b are two quantities with the same units such that ; then Ratio does not have any unit. The quantities a and b are called terms of the ratio. a' is called antecedent (first term) b' is called consequent (second te..
Definition of ratio - If a and b are two quantities with the same units such that ; then Ratio does not have any unit. The quantities a and b are called terms of the ratio. a' is called antecedent (first term) b' is called consequent (second te..Basic Definitions
Set: A well-defined collection of distinct objects is called a set. Notation of Sets: Capital letters are usually used to denote or represent a set. Representation of Sets: There are two methods of representing a set. (i) Roster Method (ii) Set builder form. ..
Definition of ratio
If a and b are two quantities with the same units such that b is not equal to zero; then the quotient a/b is called the ratio between a and b. It is written as a:b. Ratio does not have any unit. The quantities a and b are called terms of the ratio. a' is called antecedent (first term) b' is c..
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