Linear algebra is one of the important branches of mathematics. Linear algebra is basically the study of vectors and linear functions. It is a key concept for almost all areas of mathematics. Linear algebra is considered a basic concept in the modern presentation of geometry. It is mostly used in Physics and Engineering as it helps to define the basic objects such as planes, lines and rotations of the object. It allows us to model many natural phenomena, and also it has a computing efficiency. In this article, you are going to learn about the basic introduction, its components, problems, linear equations and its applications.
Introduction to Linear Algebra
Linear algebra is the study of linear combinations. It is the study of vector spaces, lines and planes, and some mappings that are required to perform the linear transformations. It includes vectors, matrices and linear functions. It is the study of linear sets of equations and its transformation properties.
Linear Algebra Equations
The general linear equation is represented as
a1x1 + a2x2……….+an xn = b
Here,
a’s – represents the coefficients
x’s – represents the unknowns
b – represents the constant
Linear Algebra Matrix
There also exists a system of linear algebraic expressions known as the linear algebra matrix. By a system of algebraic expression, we mean there is a ‘system’. One can solve this system of linear equations by using the matrices. Matrices represent systems of linear equations. Here it is essential to know that there are three kinds of elementary row operations on matrices:
Adding a multiple of one row to another row
Multiplying all entries of one row by a non-zero constant
Interchanging two rows.
Real-Life Applications of Linear Algebra
The real-life applications of linear algebra have broad applications over a wide range of fields.
Engineering, such as a line of springs.
Graphs and Networks, such as analysing networks.
Linear Programming, the simplex optimisation method.
Linear Algebra for functions, used widely in signal processing.
Computer Graphics, such as the various translation, rescaling and rotation of images.
Use of linear algebra in automated facial recognition technology.
It is also used in coding theory. One key error-correcting code is known as the hamming code.
Table of Contents:
The Course is designed specifically for those who want to learn Linear Algebra from Scratch. This is Module 1 which discusses the entire concept of Problem solving and various methods used for the same .Children often want to know 'Why they need to learn a particular concept'. So My module also gives an introduction how linear Algebra can be used in real life problems.
