Minor and Cofactor

Minor

An element, aij, to the value of the determinant of order n − 1, obtained by deleting the row i and the column j in the matrix is called a minor.

  Matrix Minor

The cofactor of the element aij is its minor prefixing:

The + sign    if  i+j  is even.

The sign    if  i+j  is odd.

Matrix Cofactor

The value of a determinant is equal to the sum of the products of the elements of a line by its corresponding cofactors:


Corresponding Cofactors  

Corresponding Cofactors

Example

Matrix Matrix Matrix Matrix

= 3(8+5) - 2(0-10) + 1(0+4) = 39 + 20 + 4 = 63