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 1.Describe the Properties of Determinant 2. Evaluate the Value of Determinant

PROPERTIES OF DETERMINANT: 1.If each entry in a row or in a column of a determinant is zero, then the value of the Determinant is zero. 2.If each entry on one side of the Principal diagonal of a Determinant is zero, then the Value of the Determinant is the product of the diagonal. 3.The value of a Determinant remains unchanged if its rows and columns are interchanged 4.If any two rows(columns) of a Determinant are interchanged, then the value of the determinant changes by minus sign only.

5.If two Parallel lines(rows or columns) of a Determinant are identical, then the value of the Determinant is zero. 6.If each entry of a row (column) of a Determinant is multiplied by the same number k, then the value of the new Determinant is k times the value of the original Determinant. 7.If each entry of a row(column) of a Determinant consists of sum of two or more terms, then the Determinant can be expressed as the sum of two or more Determinants whose other rows(columns) are not altered.

8.If to each entry of a row (column) of a Determinant be added the equimultiples of the corresponding entries of one or more rows (or columns) , the value of the Determinant remains unchanged. 9. The sum of the products of entries of any row (or column) with the cofactors of the corresponding entries of some other row(or column) is zero

EVALUATION Tell me the Properties of the Determinant.

Evaluate the following Determinant HOME WORK Evaluate the following Determinant

THANKS TO ALL, DEAR STUDENT Leibnitz, Father of Determinant