business mathematics

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations, and systems
of linear equations. Vector spaces are a central theme in modern mathematics.

Thus, linear algebra is widely used in both abstract algebra and functional analysis.
Linear algebra also has a concrete representation in analytic geometry and it is
generalized in operator theory. It has extensive applications in the natural sciences
and the social sciences, since nonlinear models can often be approximated by a linear model.

Addition and Multiplication are said to be commutative, because
A+B = B+A
A*B = B*A

Addition and Multiplication are said to be Associative, because
(A+B)+C = A+(B+C)
(A*B)*C = A*(B*C)

Multiplication is Distributive over Addition, because
A*(B+C) = (A*B)+(A*C)

here A, B, C represent any Real Number

Factorial is defined for any positive integer. It is denoted by !. Thus “Factorial n” is written as n!. n! is defined as the product of all the integers from 1 to n.

Thus n! = 1.2.3.. ... (n-1),n.

Example 5! = 1*2*3*4*5 = 120

0! is defined to be equal to 1.
Therefore 0! = 1 and 1! = 1

A decimal in which a digit is repeated continually is called a Recurring decimal. Recurring decimals are written in a shortened form, the digits which are repeated being marked by dots placed over the first and the last of them, thus




The digit, or set of digits, which is repeated is called the period of the decimal. In the decimal equivalent to 8/3, the period is 6. In 21/22 it is 54.

In arithmetic, the numbers used have definite values. These values do not change. But the letters used in algebra have no particular value and may have any value assigned to them.

Consider,
The perimeter 'p' of a rectangle of length 'l' and breadth 'b' is p = 2(l+b). Here '2' is a fixed number. The letters p, l and b have no fixed value. They can take any positive value depending upon the size of the rectangle.

So, a letter symbol which can take any value of a certain set is called a variable. Above p, l and b are variables.
Quantities which have only one fixed value are called constants. Above 2 is a constant.

What is algebra?

Algebra is one of the branches of mathematics just as arithmetic, geometry, statistics. In algebra, letters are used to represent numbers. The letters which are used to represent numbers are called literal numbers or literals. Using of literals in place of numerals helps us to think in more general terms and obtain a rule.

Consider 5*6 = 6*5 , -2*3 = 3*-2 , (1/2)*(3/4) = (3/4)*(1/2)
We can generalize the fact by the statement that the product of two rational numbers remains same in whichever order they are multiplied.
This can further be simplified by using symbols as, a*b = b*a , where a and b are any two rational numbers.