Here you will find what is matrix.what is it's application.

1. Md: Mahmudle Hassan
Department of Civil Eng.
At Daffodil International University
https://www.facebook.com/MHMMEHEDI12
Website: https://needtune.blogspot.com

2. Matrices
 A rectangular arrangement of numbers in rows and
columns.
 It is the Combination of linear equation.
 It is Represented by these symbols:
[], ||,()

3. EXAMPLE
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197
324
)a
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29
37
05
)b
 381) c 
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512
348
1097
)d
row
column column
row
row
column column
row

4. DIMENSIONS OF THE MATRIX
Row (m)
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234
012
Column(n)
A matrix with m rows and n columns is called a matrix with dimensions m x n
(# no. of row) x ( # no. of
column)
This is a 2 X 3 matrix
DIMENSIONS OF THE
MATRIX :

5. Types of Matrices
1. Row matrices – A matrices which has only one row
called row matrices e.g.-
[123]1*3
2. Column matrices – A matrices which has only one column
is called column matrices e.g. –

6. Null matrix is a matrix with all its entries being zero.

7. 123
456
789
3 ∗ 3
No of rows = No of column

8. A square matrices who’s main diagonal is ascent value ‘1’
and each of the other element is ‘0’
100
010
001
3 ∗ 3 ,
10
01
2 ∗ 2, 1 1 ∗ 1

9. A square matrices all of who’s element expect those in
the leading diagonal are ‘0’

10. A diagonal matrices in which all the elements of main
diagonal is same called scalar matrices.
3*3

11. There are two types triangular matrices ---
1.Upper triangular: All the below elements are ‘0’.
2.Lower triangular: All the above elements are ‘0’
123
045
006
3 ∗ 3
100
230
456
3 ∗ 3

12.  A matrices obtained by inter changing the rows and
columns of a matrices.
 It is denoted by A’ , AT
A⇒
123
456
789
3 ∗ 3 AT
⇒
147
258
369
3 ∗ 3

13.  Cryptography is the process of encrypting data so that
third party can’t read it and privacy can be maintained.
 It was started with the TV cable industries where even
people who were not the customer could watch the TV
programs

14.  Videocipher encryption system was invented which
would convert signals into digital form i.e. encrypt it,
and the data were send over the satellite.

15.  Since we are using a 3 by 3 matrix, we break the enumerated message
above into a sequence of 3 by 1 vectors:
 Note that it was necessary to add a space at the end of the message to
complete the last vector.
 We encode the message by multiplying each of the above vectors by the
encoding matrix.
 We represent above vectors as columns of a matrix and perform its
matrix multiplication with the encoding matrix
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27
5
20
1
9
20
15
7
5
14
27
15
20
27
5
18
1
16
5
18
16
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 
271151420185
5972727118
202051551616
434
110
433

17.  matrices are used for taking seismic surveys.
 They are used for plotting graphs, statistics and also to
do scientific studies in almost different fields.

18.  matrices are applied in the study of electrical circuits,
quantum mechanics and optics.
 In the calculation of battery power outputs, resistor
conversion of electrical energy into another useful
energy, these matrices play a major role in
calculations.
 Especially in solving the problems using Kirchoff’s
laws of voltage and current, the matrices are essential.

19.  First, write a numerical value for each letter i.e. A=1,
B=2, and Z=26, and space=27.
 The data should be placed in matrix form i.e. in 2x1 or
3x1 matrix form.

20.  The data should be multiplied by given encoding
matrix.
 Then, write the answer (value after multiplying) in
linear form. How to encrypt data? Encryption Process

21.  matrices play a vital role in the projection of three
dimensional image into a two dimensional screen,
creating the realistic seeming motions.
 Stochastic matrices and Eigen vector solvers are used
in the page rank algorithms which are used in the
ranking of web pages in Google search.

22.  The matrix calculus is used in the generalization of
analytical notions like exponentials and derivatives to
their higher dimensions.
 One of the most important usages of matrices in
computer side applications are encryption of message
codes.
 Matrices and their inverse matrices are used for a
programmer for coding or encrypting a message.

23.  Matrices are used in representing the real world data’s like the traits of people’s
population, habits, etc.
 They are best representation methods for plotting the common survey things.
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 • Matrices are used in calculating the gross domestic products in economics which
eventually helps in calculating the goods production efficiently.
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 • Matrices are used in many organizations such as for scientists for recording the data
for their experiments.
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 • In robotics and automation, matrices are the base elements for the robot movements.
 The movements of the robots are programmed with the calculation of matrices’ rows and
columns.
 The inputs for controlling robots are given based on the calculations from matrices.