WELCOME TO THE HIGHER MATHEMATICS CLASS
SHIPAN CHANDRA DEBNATH
ASSISTANT PROFESSOR
&
HEAD OF THE DEPARTMENT
DEPARTMENT OF MATHEMATICS
CHITTAGONG CANTONMENT PUBLIC COLLEGE
[email protected]
Today`s Topics is
DETERMINANT
Chapter - 1
Exercise -1(B)
Book: Higher Mathematics
Akkhorpotra Publications
Learning Outcomes
After complete this class students can
1. Explain singular and non-singular matrices
2. Explain Inverse of square matrix
3. Solve the linear equations by Determinant
Symmetric matrix : A square matrixA=[aij] is said to be a
symmetric matrix if aij=aji for all i and j . For example
1 3 
A

3 0
A square matrix A is symmetric iff A  A
Skew Symmetric matrix : A square matrixA=[aij] is said
to be a skew symmetric matrix if aij=-aji for all i and j .
For example
3
0
A

 3 0 
A square matrix A is skew symmetric iff A   A
note : A skew symmetric matrix all entries along the
principal diagonal are zero.
Orthogonal matrix : A matrix A is said to be Orthogonal
iff AA`=I ,where A` is the Transpose of A.For example
cos 
A
sin


 sin  

cos  
Singular matrix : If the Determinant value of the square
matrix is zero , then matrix is called singular matrix . For
example
4 6 
A

2
3


Non-Singular matrix : If the Determinant value of the
square matrix is nonzero , then matrix is called nonsingular matrix . For example
1
A
2

5

7
Transpose of a matrix : Let A be any matrix then the
matrix obtained by interchanging its rows and columns is
called the Transpose of a Matrix A and is denoted by A`
or AT. For example
1
if A  
2

5

7
1

T
then A  
5

2

7
Cofactor matrix : Let A=[aij] be a square matrix. Let
B=[Aij] where Aij is the cofactor of the entry aij in the
matrix A. The matrix B is called cofactor matrix of the
matrix A. For example
1
A
2
5
7  2 
then
cofactor
of
A

B




7
 5 1 
Adjoint of square matrix : Let A=[aij] be a square matrix.
Let B=[Aij] where Aij is the cofactor of the entry aij in the
matrix A. The Transpose B` of the matrix B is called the
adjoint of the matrix A. For example
1
A
2
5
 7  5
then
adj
of
A

B
`




7
 2 1 
Inverse or Reciprocal of a square matrix : Let A=[aij] be
a square matrix of order n. Then a matrix B is called the
inverse of A iff AB=BA=In inverse of the square matrix
A is denoted by A-1
1
A
2
5
7

5


adjA
1
1
then
A





7
A
 3  2 1 
EVALUATION
1. Tell the definition of cofactor matrix, adjoint
matrix and inverse matrix.
HOME WORK
0

1. find the inverse of A  1

3
2

2 3
1 1

1
THANKS TO
ALL,
DEAR
STUDENT
Leibnitz, Father of Determinant