Introduction to Linear Algebra

Linear Algebra is one of the branches of Mathematics.  These helps with the study of vectors, vector spaces, linear transformations, and systems of linear equations. Vector spaces are found in modern math thus, it is widely used in both abstract algebra and functional analysis.
It is also found in solving problems in analytic geometry.
 Its application is found extensively  the natural sciences and the social sciences.  This forms an intro to Linear Algebra.

 The mathematical approach of solving for variables in equations is Algebra.  
It does the manipulation of these variables using mathematical structures.
It is like taking algebra to another level by manipulating these variables using mathematical structures. This also helps to write the entire system of equations in the form of matrices. When expressed in the form of matrices this to study in depth of the individual parts of matrix which is known as vertex. A vertex is simply a representation of a coordinate.

Linear algebra is a branch of mathematics.  The creation of analytic geometry led to  the system of linear equations  acquire a new significance.
Linear-algebra is important for both pure mathematics and applied mathematics.    
Linear form of algebra when combined with calculus facilitates the solution of linear systems of differential equations.

Analytic geometry, engineering, physics, natural sciences, computer science, and the social sciences   use the techniques of Linear-algebra.
Linear mathematical models are sometimes used to approximate Non-linear mathematical models because linear algebra is such a well-developed theory.
The real world applications need Linear-Algebra.  Algebra is all about linear system of equations and their solutions Linear-Algebra usually consists of the linear set of equations as well as their transformations on it.  Linear Equations  consists of  topics  like  Linear Equations , Matrices, Determinants, Complex numbers, Second degree equations, Eigen values ,Linear Transformations.

Linear algebra help to mathematics: It is a useful branch of mathematics.   Below listed is some of the applications of Linear form of Algebra.  Constructing curves, Least square approximation, traffic flow, Electrical circuits, Determinants, Graph theory, Cryptography.
It   is used to draw graphs. Most equations of linear algebra will   be a straight line. For example draw a graph for a vehicle travelling at a constant speed at various time intervals.
The graph helps in determining the    unknown variable that is the distance by plotting in on the graph.  This can also be used for   a multitude of different functions that is a ready tool for  lots of different real life functions.