Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is

Step-by-step solution

Given the elements of the 3 3 matrix A = [a_ ij ] : For the diagonal elements ( i = j ): a₁₁ = 1 - 2(1) = -1 a₂₂ = 2 - 2(2) = -2 a₃₃ = 3 - 2(3) = -3 For elements below the principal diagonal ( i > j ): a₂₁ = 0, a₃₁ = 0, a₃₂ = 0 For elements above the principal diagonal ( i a₁₂ = 1, a₁₃ = 1, a₂₃ = 1 Constructing the matrix A , we get: A = bmatrix -1 & 1 & 1 0 & -2 & 1 0 & 0 & -3 bmatrix Since A is an upper triangular matrix, its determinant is simply the product of its principal diagonal elements: |A| = (-1) (-2) (-