Cofactor Matrix

The cofactor of an element, aij, is its minor prefixing:

+ sign    if  i+j  is even.

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 multiplied 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





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