Determinants

Notes

ntroduction: and expansion of determinant Minors and Cofactors Properties of determinants, Maximum and Minimum values of a determinant. Product of determinants, Deff representation of determinants. Some special Determinants, System of Linear Equations, Area of triangle using Determinants. Concurrency of straight lines. Critical Topics in the chapter:- → Properties 5 and 6 of determinants. → System of Linear Equations. Determinant with n-Rows and n-columns.

Note:- In a determinant, number of Rows and number of Columns are always equal. Order of a determinant

Value of a determinant

→ Minors and Cofactors:

Similarly

C21=2

Observation

2. If two rows or columns of a determinant are interchanged then the determinant retains its absolute value but its sign is changed.

8. the sum of the products of the elements of any row (column) of a determinant with cofactors of the corresponding elements of any other row(column) is zero.