Matrix A = bmatrix 1 & 1 & 2 1 & -2 & 2 1 & 0 & -1 bmatrix , Given M₂₂ and A₃₂ are the minor and cofactor of the adjoint matrix of A respectively then the value of the expression M₂₂ + A₃₂ - |adj A| is:

Step-by-step solution

The given matrix is A = bmatrix 1 & 1 & 2 1 & -2 & 2 1 & 0 & -1 bmatrix . First, we find the determinant of matrix A : |A| = 1((-2)(-1) - (2)(0)) - 1((1)(-1) - (2)(1)) + 2((1)(0) - (-2)(1)) |A| = 1(2) - 1(-3) + 2(2) = 2 + 3 + 4 = 9 Using the property of the adjoint of a matrix, |adj A| = |A|^ n-1 . For a 3 3 matrix, n = 3 : |adj A| = |A|³⁻¹ = 9^2 = 81 Let B = adj A . We need to find the minor M₂₂ and cofactor A₃₂ of matrix B . Let C be the cofactor matrix of B . By definition, adj B = C^T , which implies C = (adj B