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