1. WELCOME TO THE HIGHER MATHEMATICS CLASS
SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE

2. DETERMINANT Today`s Topics is Chapter - 1 Exercise -1(B)
Book: Higher Mathematics
Akkhorpotra Publications

3. Learning Outcomes After complete this chapter students can
1.Definition of Determinant
2. Explain Minor and Cofactor
3. Evaluate the Value of Determinant

4. On Eliminating the variables x and y from the system (1) , we get
Let us consider the following system of equations
a1x+b1y=0
a2x+b2y=0 in the two variables x and y . From these equations, We obtain
On Eliminating the variables x and y from the system (1) , we get

6. The above eliminate is written as
The left hand side of (2) is called a Determinant of order 2.
A Determinant of order n is an arrangement of nn in the form of a square along n Horizontal lines called rows and along vertical lines called columns and these numbers are enclosed within two vertical lines.

7. Cofactor and Minor : Let
be a Determinant of order n,n 2, then determinant of order n-1 obtained from the determinant D after deleting the ith row and jth column is called the minor of the element aij and it is, usually denoted by Mij where i=1,2,3,…m and j=1,2,3,…n.
If Mij is the minor of the element aij in the Determinant D, then the number (-1)i+jMij is called the Cofactor of the element aij, it is usually denoted by Aij

8. Evaluating the value of Determinant: there are three rules are important to evaluate the value of the Determinant. These are
Sarrus Method
Co-factor Method
Operating Method

9. EVALUATION
Tell me the Definition of Minor and Cofactor

10. Evaluate the following Determinant by three process
HOME WORK
Evaluate the following Determinant by three process