for the matrix

Question

 

A =[aij]=         -8       1       5

                       15      15     -8

                       3       14      -4

 

a) find the minor of the element a₂₁

b) find the co-factor of the element  a₂₁

 

The minor is

The co-factor is  

Answer 1

The minor of a₂₁ is the determinant of the matrix obtained by deleting row 2  and column 1:  

 

              1      5

     det                 = (1)(-4)-(5)(14) = -4 - 70 = -74

             14    -4

 

The cofactor of a₂₁ is the minor obtained above times (-1)²⁺¹ = -1

 

     So, cofactor of a₂₁ = 74