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 class students can
Explain singular and non-singular matrices
Explain Inverse of square matrix
Solve the linear equations by Determinant

4. Symmetric matrix : A square matrixA=[aij] is said to be a symmetric matrix if aij=aji for all i and j . For example

5. 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

6. Orthogonal matrix : A matrix A is said to be Orthogonal iff AA`=I ,where A` is the Transpose of A.For example

7. Singular matrix : If the Determinant value of the square matrix is zero , then matrix is called singular matrix . For example

8. Non-Singular matrix : If the Determinant value of the square matrix is nonzero , then matrix is called non-singular matrix . For example

9. 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

10. Cofactor matrix : Let A=[aij] be a square matrix
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

11. Adjoint of square matrix : Let A=[aij] be a square matrix
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

12. 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

13. EVALUATION
Tell the definition of cofactor matrix, adjoint matrix and inverse matrix.

14. HOME WORK

15. THANKS TO ALL,
DEAR STUDENT
Leibnitz, Father of Determinant