Title: Some Application of Matrix

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CONTENTS

• What are Matrices?
• Types of Matrices
• Application of Matrices

Use of Matrices in Computer Graphics

Use of Matrices in Wireless Comunication

Use of Matrices in Science

Use of Matrices in Finding Area of Triangle

Use of Matrices for Collinear Point

• Conclution
• Reference

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WHAT ARE MATRICES?

• A matrix is defined as a rectangular array of numbers or symbols which are generally arranged in rows and columns.
• The order of the matrix can be defined as the number of rows and columns.
• The entries are the numbers in the matrix known as an element..
• The size of a matrix is denoted as ‘n by m’ matrix and is written as m×n, where n= number of rows and m= number of columns.
• Example:

The matrix given above has 2 rows and three columns.

4 9 17

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5 71 23

A =

TYPES OF MATRIX:

• There are different types of matrices. Here they are –
• 1)Row matrix
• 2) Column matrix
• 3) Null matrix
• 4) Square matrix
• 5) Diagonal matrix
• 6) Upper triangular matrix
• 7) Lower triangular matrix
• 8) Symmetric matrix
• 9) Skew-symmetric matrix

APPLICATIONS OF MATRICES:

• Matrices have many applications in diverse fields of science, commerce and social science. Matrices are used in:
• (i)Computer Graphics
•  (ii) Optics 
• (iii) Cryptography 
• (iv) Economics
• (v) Chemistry 
• (vi) Geology 
• (vii) Robotics and animation 
• (viii) Wireless communication and signal processing 
• (ix) Finance ices
• (x) Mathematics

USE OF MATRICES IN COMPUTER GRAPHICS:

• Square matrices very easily represent linear transformation of objects. They are used to project three dimensional images into two dimensional planes in the field of graphics.

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USE OF MATRICES IN WIRELESS COMMUNICATION:

• Matrices are used to model the wireless signals and to optimize them. For detection, extractions and processing of the information embedded in signals matrices are used.

USE OF MATRICES IN SCIENCE:

• Matrices are used in science of optics to account for reflection and for refraction. Matrices are also useful in electrical circuits and quantum mechanics and resistor conversion of electrical energy.

APPLICATION OF MATRICES IN MATHEMATICS:

• Application of matrices in mathematics have an extended history of application in solving linear equations. Application of matrices in mathematics applies to many branches of science, also as different mathematical disciplines.

Use of Matrices in Finding Area of Triangle:

• We can use matrices to find the area of any triangle where the vertices of the triangle have been given.

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• Area of the triangle ABC given by The determinant

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= ½ ×

a b 1

c d 1

e f 1

USE OF MATRICES FOR COLLINEAR POINT:

• Matrices can be used to check where any three given points are collinear or not.
• The point A,B,C are colinear if vanishes.

a b 1

c d 1

e f 1

the matrix we are is useful and powerful in the mathematical analysis and collecting data. Besides the simultaneous equations, the characteristic of the matrices are useful in the programming where we putting in array that is a matrix also to store the data. With this mini project, we know more about matrix and if we need to know all about how it uses in the computer science subject, I personally think that it will be difficult as it can be very complicated.

CONCLUSION:

REFERENCE:

https://www.google.com/url?sa=t&source=web&rct=j&url=https://en. m.wikipedia.org/wiki/Matrix_(mathematics)&ved=2ahUKEwjehe2- wKv1AhWKSmwGHWYJB50QFnoECAQQAQ&usg=AOvVaw2hogn yI7zYy6bdjsuoc9P2

Higher Algebra-S. K. MAPA

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THANK YOU TO ALL