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

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

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

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

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.

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

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

EVALUATION Tell me the Definition of Minor and Cofactor

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