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MATRICES &
DETERMINANTS
Background:
MATRICES:
Types Of Matrices:
 Row Matrix:
A matrix having single row is called Row Matrix.
e.g.
B=[1 4 6]
 Column Matrix:
A matrix having single column is called
column Matrix.
e.g.
1
A= 4
7
 Square Matrix:
A matrix in which no of rows and columns are
equal is called square matrix.
e.g.
2 3
B=
1 7
 Rectangular Matrix:
A matrix in which no of rows and columns are
not equal is called square matrix.
e.g.
D= 1 4 6
7 3 1
 Diagonal Matrix:
A square matrix having each of its elements
excepts principle diagonal equal to zero and
at least one elements in its principle diagonal
matrix.
e.g.
1 0 0
S= 0 2 0
0 0 3
 Zero Matrix:
A square or rectangular matrix whose each element is zero, is called a null
or zero matrix.
It is denoted by O(m×n).
e.g.
O2×2=
0 0
0 0
 Scalar Matrix:
A square matrix having same elements in
principle diagonal except 1 is called scalar
matrix.
e.g.
k 0 0
A= 0 k 0
0 0 k
 Unit or Identity Matrix:
The identity matrix of size n is
the n × n square matrix with ones on
the main diagonal and zeros elsewhere. It is
denoted by In or simply by I.
1 0 0
I= 0 1 0
0 0 1
 Equal Matrix:
Two matrix are said to be equal if they are of
same order with the same correspondence
elements.
e.g.
3 5 3 5
A= B=
3 0 3 0
 Triangular Matrix:
UpperTriangular Matrix:
If all elements below the principle diagonal of
square matrix are zero then it is called upper
triangular matrix.
1 4 6
B= 0 1 3
0 0 1
 Triangular Matrix:
LowerTriangular Matrix:
If all elements above the principle diagonal of
square matrix are zero then it is called lower
triangular matrix.
1 0 0
B= 0 1 0
2 4 6
Operation of Matrices:
Problem for Practice:
Chapter 3-Introduction-.pptx

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Chapter 3-Introduction-.pptx