The cofactor of the element a₂₁ in the expansion of = | array ccc 1 & 4 & 4 -3 & 5 & 9 2 & 1 & 2 array | is

Step-by-step solution

The element a₂₁ is the element in the second row and first column of the determinant = vmatrix 1 & 4 & 4 -3 & 5 & 9 2 & 1 & 2 vmatrix . The value of a₂₁ is -3 . The cofactor C_ ij of an element a_ ij is given by (-1)^ i+j M_ ij , where M_ ij is the minor obtained by deleting the i -th row and j -th column. For a₂₁ , we have i=2 and j=1 . Thus, the cofactor is C₂₁ = (-1)²⁺¹ M₂₁ = -M₂₁ . The minor M₂₁ is the determinant of the matrix formed by removing the second row and first column: M₂₁ = vmatrix 4 & 4 1 & 2 vmatri