Minors And Cofactors
Minor of an element aij of a determinant is the determinant obtained by deleting its ith row and jth column in which element aij lies. Minor of an element aij is denoted by Mij.
eg given the follwing matrix A,
Minor of element a1= ( b2 * c3 ) - ( c2 * b3 )
eg a Matrix A =
Minor of element a13 ie 4 is =
Thus value of Minor = 7*8 - 6*3 = 38
Cofactor of an element aij , denoted by Aij is defined by Aij = (–1)^(i + j) * Mij , where Mij is minor of aij.
eg Given the Matrix A,
at i=1,j=3 element =3
Minor of A(1,3) = 7*8 - 6*3 = 38
Thus Cofactor of A(1,3) = [ (-1)^(1+3)] * 18 = 18