Write Minors and Cofactors of the elements of following determinants:
Minor: Minor of an element aij of a determinant is the determinant obtained by removing ith row and jth column in which element aij lies. It is denoted by Mij.
Cofactor: Cofactor of an element aij, Aij = (-1)i+j Mij.
Minor of element aij = Mij
a11 = 2, Minor of element a11 = M11 = 3
Here removing 1st row and 1st column from the determinant we are left out with 3 so M11 = 3.
Similarly, finding other Minors of the determinant
a12 = -4, Minor of element a12 = M12 = 0
a21 = 0, Minor of element a21 = M21 = -4
a22 = 3, Minor of element a22 = M22 = 2
Cofactor of an element aij, Aij = (-1)i+j × Mij
A11 = (-1)1+1 × M11 = 1 × 3 = 3
A12 = (-1)1+2 × M12 = (-1) × 0 = 0
A21 = (-1)2+1 × M11 = (-1) × (-4) = 4
A22 = (-1)2+2 × M22 = 1 × 2 = 2