Types of Matrics

11 types of Matrics. For Grade 11 and more

1. Types of Matrices
Narmatha Devi N
Mathematics
Grade 11

2. Here, we will be seeing about some different types of
matrices.
About…

3. •What is a matrix ?
•What is an order of the matrix ?
Recap…

4. •Amatrixisarectangulararrayorarrangementofentriesor
elementsdisplayedinrowsandcolumnsputwithinasquare
bracket[].
•IfamatrixAhasmrowsandncolumns,thenitiswrittenas
�=�
��
��
1≤�≤�,1≤�≤�
Matrix

5. •IfamatrixAhasmrowsandncolumns,thentheorderorsize
ofthematrixAisdefinedtobe��(readasmbyn).
OrderoftheMatrix
�=
497
261
The Matrix Ais of order 2×3
Example

6. TypeofMatrices…
▪RowMatrix
▪ColumnMatrix
▪ZeroMatrix
▪NonZeroMatrix
▪SquareMatrix
▪DiagonalMatrix
▪ScalarMatrix
▪UnitMatrix
▪UpperTriangularMatrix
▪LowerTriangularMatrix
▪TriangularMatrix

7. •Amatrixhavingonlyonerowiscalledarowmatrix
•�=�
1�
1�
isarowmatrixoforder1�
RowMatrix
�=47 �=293 �=����

8. •Amatrixhavingonlyonecolumniscalledacolumnmatrix
•�=�
�1�×1isarowmatrixoforder�×1
ColumnMatrix
�=
5
9
�=
�
�
�
�=
6
7
3
9

9. •Amatrix�=�
��
��
issaidtobeazeromatrixornull
matrixorvoidmatrixdenotedbyOif
�
��=0for all values of1≤�≤�and 1≤�≤�
ZeroMatrix/NullMatrix/VoidMatrix
�=
00
00
�=
000
000
�=
0
0
0

10. •AmatrixAissaidtobeanon-zeromatrixifatleastoneofthe
entriesofAisnon-zero
NonZeroMatrix
�=25 �=
60
00
�=
2.59.2
0
3
5
8 0

11. •Amatrixinwhichnumberofrowsisequaltothenumberof
columns,iscalledasquarematrix.
•i.e,amatrixoforder�×�isoftenreferredtoasasquare
matrixofordern.
SquareMatrix
�=
12
34
�=
111213
212223
313233

12. •Inasquarematrix�=�
��
��
ofordern,theelements
�
11,�
22,�
33,…�
��arecalledtheprincipaldiagonalor
simplythediagonalormaindiagonalorleadingdiagonal
elements.
SquareMatrix–theprincipaldiagonal
�=
56.23.5
4.876
1291
,
Here, the principal diagonal elements is 5,7,1

13. •Asquarematrix�=�
��
��
issaidtobeadiagonalmatrixif
�
��=0whenever i≠�
DiagonalMatrix
�=
200
050
006
�=
�0
0�
�=
000
000
000
Note : A square zero matrix is a diagonal Matrix

14. •Adiagonalmatrixwhoseentriesalongtheprincipaldiagonal
areequaliscalledaScalarmatrix.
•Asquarematrix�=�
��
��
issaidtobeaScalarmatrixif
�
��=ቊ
��??????�=�
0�??????�≠�
,wherecisafixednumber
ScalarMatrix

15. ScalarMatrix
Note:Anysquarezeromatrixcanbeconsideredasascalar
matrixwithscalar0
�=
500
050
005
�=
120
012
�=
000
000
000

16. •Asquarematrixinwhichallthediagonalentriesare1andthe
restareallzeroiscalledaunitmatrix.
•A square matrix�=�
��
��
is said to be a unit matrix if
�
��=ቊ
1�??????�=�
0�??????�≠�
UnitMatrix
�=
100
010
001
�=
10
01

17. •Asquarematrixissaidtobeanuppertriangularmatrixifall
theelementsbelowthemaindiagonalarezero.
•Asquarematrix�=�
��
��
issaidtobeanuppertriangular
matrixif�
��=0forall�>�
UppertriangularMatrix
�=
18507
016
0019
�=
110
016
�=
71890
0124
0035

18. •Asquarematrixissaidtobeanlowertriangularmatrixifall
theelementsabovethemaindiagonalarezero.
•Asquarematrix�=�
��
��
issaidtobealowertriangular
matrixif�
&#3627408470;&#3627408471;=0forall&#3627408470;<&#3627408471;
LowertriangularMatrix
&#3627408436;=
9100
451.10
2.55.382
&#3627408437;=
50
91
&#3627408438;=
2400
380
572

19. •Asquarematrixwhichiseitheruppertriangularorlower
triangulariscalledatriangularmatrix
TriangularMatrix
Note:Asquarematrixthatisbothupperandlowertriangular
simultaneouslywillturnouttobeadiagonalmatrix
&#3627408436;=
500
740
839
&#3627408437;=
895
046
002
&#3627408438;=
500
050
005

20. TypeofMatrices…
▪RowMatrix
▪ColumnMatrix
▪ZeroMatrix
▪NonZeroMatrix
▪SquareMatrix
▪DiagonalMatrix
▪ScalarMatrix
▪UnitMatrix
▪UpperTriangularMatrix
▪LowerTriangularMatrix
▪TriangularMatrix

21. Identifythetypeofeachmatrix:
&#3627408436;=
123
046
007
&#3627408437;=
&#3627408485;
&#3627408486;
&#3627408487;
&#3627408438;=
100
010
001
&#3627408439;=
20
02
Testingtime…

22. ThankYou…