Co Factors

By the co factor of an element of a matrix we mean the product of  (-1)^i+j and the minor of the concerned element (M_ij)

Where  C_ij  = the co factor of the element in the ith row and jth column of the matrix.

(-1)^i+j =the factor determining the algebraic sign depending upon the number of row (i) and number of column (j) in which the element occurs in the matrix.

M_ij = the minor of the element in the ith row and jth column of the matrix.

Thus, C₁₁ = (-1)¹⁺¹, m₁₁; c₁₂ = (-1)¹⁺². M₁₂, and c₁₃ = (-1)¹⁺³. M₁₃

Minor

By the minor of an element of a matrix we mean the sub square-matrix of the given matrix along which the particular element (e_ij) does not exist. It is obtained by deleting the row and the column on which the particular element (e_ij) lies. It is representing by M_ij, which denotes the minor of an element in the ith row and jth column of the matrix. Its value is obtained by deducting the product of its non-leading diagonal elements from the product of its leading diagonal elements.

Examples: