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Govt. polytechnic college
Bhatapara
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Branch – Civil(B)
Seminar on
Matrices
Guided By:
Divya Jotwani Mam
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Presented By :
Devendra and Anshul
Contents
0011 0
0 1 0 1 0 1of
1 0matrix
1 0001 0100 1011
0 1Definition
Types of matrix
• Row matrix
• Column matrix
• Null matrix
• Square matrix
• Unit (identity) matrix
Addition and subtraction of Matrices
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Definition of matrix :- A set of mn number (real or complex) arranged in a rectangular array of m
rows(horizontal lines) and n column (vertical lines) is called a matrix of order m × n. A matrix of order m by n of mn
0 0 1 1 0is
0 usually
10 101
0 110
1 1 𝑎13 … 𝑎14
elements
written
as1 0 0 0 1 0 1 0𝑎011 1 0𝑎12
𝑎21 𝑎22
…… ……
… …
𝑎𝑚1 𝑎𝑚2
𝑎23 …
…
… ……
𝑎24
…
…
… …
𝑎𝑚3 …
…
𝑎𝑚𝑛
Where it has m rows and n column
A matrix generally denoted by single capital letterAor B or C etc. Thus , an m×nmatrix A may be written as
A= 𝑎𝑖𝑗 m×n
A= 𝑎𝑖𝑗
i=1,2,3......m, j =1,2,3.....n
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Types of matrix
• (a) Row of Matrix : If a matrix has only one row and any number of column ,
row
0 0 1 1 0 0 1it0 is
1 called
0 1 0 1a
10
1 0matrix
0 0 1 0 ,e.g.,
100 1011
• 3582
• (b) Column of Matrix : A matrix , having one column and any number of rows
,is called a column matrix ,.e.g..,
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• (c) Null Matrix (Zero Matrix): Any matrix in which all the elements are zero ,
0 0 0
is called a zero or null matrix e.g., 0 0 0
0 0 0
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•(d) Square matrix : A square matrix , in which the number of rows is equal to the
number of column ,is called , a square matrix e.g.,
7 9
3 4
0011 0010 1010 1101 0001 0100 1011
• (e) Unit identity matrix: A square matrix is called a unit matrix if all the diagonal
elements are unity and non diagonal elements are zero e.g.,
1 0 0
1
0 1 0
0
0 0 1
0
1
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Addition and subtraction of matrices:
Two matrices are said to be conformable for addition if they are of the are of the same
0011 0010 1010 1101 0001 0100 1011
order (i.e., number of rows and column are equal ).
The addition A+B is defined as matrix whose each elements
is the sum of the corresponding elements of A and B.
In general ,if
Then
A= aij mxn and B= bij mxn
A+B=Ccij mxn where cij=aij + bij
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Similarly, if A and B are two matrices of the same order then their difference A-B is a
matrix whose elements are obtained by subtracting the elements of B from the
corresponding elements of A.
In general ,if
A= aij mxn and B= bij mxn
Then
A-B=Ccij mxn where cij=aij - bij
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