Linear Algebra

Hello friends, today we are going to learn algebra that is used to study about the set of linear equations.

Linear equation in terms of n variables is shown as a₁x₁+a₂x₂+......+a_nx_n=b. Where a₁,a ₂ up to a_n and b are the real numbers.

Example : a₁=2, a₂=3 and b=6 then equation will be 2x+3y=6 that describes the line passing through points (2,0) (0,3).

Matrices and determinants are most useful thing in the linear algebra. you can get more help on algebra here

Solutions of an equation with the help of matrices:

The equation is expressed as Ax=B. By solving the equation we get x in terms of inverse matrix as x=A^-1.B. Here A^-1 is showing the inverse matrix of A.

A vector space is a set V with two binary operations over a field that satisfies the axioms of the algebraic equation. In the vector space V and the operation of addition, multiplication etc follows some axioms as :-

Associativity of addition : a+(b+c)=(a+b)+c

Commutativity of addition : a+b=b+a

Identity element of addition : Є V as V+0=V

Inverse elements of addition as For every v ∈ V, there exists an element −v ∈ V, called the inverse element v such as v+(-v)=0

Here also some rules related with the multiplication :

Distributativity of scaler multiplication of a vector addition : a(b+c)=ab+ac

Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv

Identity element of scalar multiplication 1v = v, where 1 denotes the multiplicativity identity.

In upcoming posts we will discuss about Math Blog on How to Solve Linear Equations and Base angle. Visit our website for information on secondary school education Andhra Pradesh

Application of Linear Algebra

Linear algebra on the whole is studying about the set of linear equations. These problems are specified in mathematics, physics, and also in engineering.
Linear algebra deals with vector space. A vector space is a set K with two binary operations over a field that satisfies the axioms of the algebraic equation. In the vector space K and the operation of addition, multiplication etc follows some axioms as:-
Associatively of addition, a+(b+c)=(a+b)+c
Matrix and determinant are most useful thing in the linear algebra. The main problem of linear algebra is solution of the matrix. The linear algebra solution is expressed as Ax=B. By solving the equation we get x in terms of inverse matrix as x=A-1.B. Here A-1 is showing the inverse matrix of A. Linear equation in terms of n variables is shown as a1x1+a2x2+......+anxn=b, where a1,a 2 up to an and b are the real numbers.
We will understand it by an example or you can use online tools like linear equation calculator.
If a1=2, a2=3 and b=6 then equation will be 2x+3y=6 that describes the line passing through points (2, 0) (0,3).

Applications of linear algebra are following:-
1.      Linear algebra is used in different areas like:-abstract thinking, games, cryptography, economics, image compression etc.
2.      In cryptography, people concerned with private communication use the encryption and decryption method with the secret key. Fundamentally it is used for security purpose.
3.      Linear algebra is also used in image compression. It is used in compressing digital images and it takes less space when stored and transmitted.
4.      Linear programming is another approach to linear algebra problems. We will see in which way we are maximizing or minimizing a linear expression in any number of variables with some linear constraints. This technique is used in a wide range of problems in industry and science.

In upcoming posts we will discuss about Linear Algebra and Vertex angle. Visit our website for information on board of intermediate education Andhra Pradesh