-
8/17/2019 37706484-Matrices.pptx
1/10
MA T R I C E
S
-
8/17/2019 37706484-Matrices.pptx
2/10
MATRICES
Definition : A matrix is a rectangular array of
numbers of functions enclosed in brackets.Tese numbers of
functions are called
entries or elements of te matrix.
-
8/17/2019 37706484-Matrices.pptx
3/10
!E"ERA# "$TATI$" $% A MATRI&
A ' ( a )k* '
A matrix is al+ays denoted by ca,ital letter
-
8/17/2019 37706484-Matrices.pptx
4/10
T-ES $% MATRICES
S/0ARE MATRI&:1 If te number of ro+s of amatrix is e2ual to
number of columns ten suc a
matrix is kno+n as a s2uare matrix. %or exam,le
A '
RECTA"!0#AR MATRI&:1 If te matrix is not a
s2uare matrix ten it is called a rectangular matrix.
%or exam,le A '
Continue..........
-
8/17/2019 37706484-Matrices.pptx
5/10
DIA!$"A# MATRI&:1 A s2uare matrix in +ic allte elements on
te main diagonal are non13ero.
Any entries abo4e or belo+ te main diagonal must
be 3ero.
e.g. A '
IDE"TIT- MATRI&:1 In te diagonal matrix all te
elements are e2ual to unity. It is denoted by I.
e.g. I '
Continue……….
-
8/17/2019 37706484-Matrices.pptx
6/10
SI"!0#AR MATRI&:1 If te 4alue of tedeterminant of te matrix
is 3ero ten it is
called singular matrix.
i.e. 5A5 ' 6.
TRA"S$SITI$" $% MATRI&: In m x n
matrix first ro+ of a matrix as its first column7
te second ro+ as its second column7 and so
on. It is denoted by A8 or AT
Continue……….
-
8/17/2019 37706484-Matrices.pptx
7/10
S-MMETRIC MATRI&:1 If te trans,ose of a matrixis e2ual to te
gi4en matrix ten it is called
symmetric matrix. i.e. AT ' A
S9E1S-MMETRIC MATRI&:1 If te trans,ose ofa matrix is e2ual
to te minus of gi4en matrix ten
it is called ske+1symmetric matrix. i.e. AT ' 1 A
-
8/17/2019 37706484-Matrices.pptx
8/10
!eneral conce,ts
MATRI& ADDIT$":1 Addition is defined only formatrices
A and ; of te same si3e< teir sum
+ritten A=;7 is ten obtained by adding te
corres,onding elements.
SCA#R M0#TI#ICTI$":1 Te ,roduct of any m
x n matrix A and any scalar c7 +ritten as cA7 is te
m x n matrix cA obtained by multi,lying eac
element in A by c.s
MATRI& M0#TI#ICATI$":1 Te ,roduct C ' A; ofan m x n matrix A
and r x , matrix is defined if and
only if r ' n. tat is.
Number of columns of A = Number of rows of B.
-
8/17/2019 37706484-Matrices.pptx
9/10
A#ICATI$" $% MATRICES
e can sol4e te system of liner e2uations usingmatrix metod.
;y finding te rank of matrix +e can talk about te
existence of te solution of te system
-
8/17/2019 37706484-Matrices.pptx
10/10
