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..
Complex Numbers
Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex ..
Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex ..Matrices
A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracke..
Matrices and Determinants
Matrices - A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracke..
Introduction
Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number h..
Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number h..Question 2
Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there are infinite numb..
Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there are infinite numb..Real Numbers
Real Numbers - The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real numbers..
Real Numbers - The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real numbers..
Consistency and Inconsistency of a System of Linear Equations
A system of linear equations is said to be consistent if it has a solution. This means that the solution satisfies all the equations in the system simultaneously. If a system of linear equations has no solution, then it is said to be inconsiste..
Note:
Set of real numbers is a proper subset of the set of Complex numbers..
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