Maths concept note from NCERT: Properties of Determinants
BY Team Aakash Byju's
Determinant is defined as a property of a “system of linear equations.” The determinant ‘determines’ whether the system has a unique solution or not.Determinant is denoted by Delta or D.
Sign system for order 2, order3, order4,…are shown above.The qualities of determinants are based on the elements, row, and column operations, and they aid in finding the determinant's value quickly.
Property 1 (interchange property):The value of determinant remains same, if it's rows and columns are interchanged.
Property 2 (sign property):If any two rows or columns of a determinant are interchanged, the sign of determinant will be changed.But, the numerical value remains unaltered.
Property 3 (Zero property):If the elements in any two rows or columns are the same, the determinant's value is zero.
Property 4If all elements of any row or any column are zero, the determinant value becomes zero.
Property 5 (multiplication property)If each element of a given row or column is multiplied by a constant k, then the value of the new determinant is k times the value of the original determinant.
Property 6 (sum property)If each element of any row or column consists of two terms, then the determinant can be expressed as the sum of two other determinants.
Property 7If all elements of below diagonal or above diagonal or except diagonal elements are zero, then the value of the determinant is equal to product of all diagonal elements.