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 class students can Explain singular and non-singular matrices Explain Inverse of square matrix 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

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

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

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

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

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

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

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

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

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

HOME WORK

THANKS TO ALL, DEAR STUDENT Leibnitz, Father of Determinant