If A = [a_ ij ]_ 3 3 is a matrix such that a_ ij = |2i - 5j| , where |.| denotes the modulus function, then the element in the 2^ nd row and 3^ rd column of A⁻¹ is ...

Step-by-step solution

Given a_ ij = |2i - 5j| , we construct the matrix A of order 3 3 : A = bmatrix |2(1)-5(1)| & |2(1)-5(2)| & |2(1)-5(3)| |2(2)-5(1)| & |2(2)-5(2)| & |2(2)-5(3)| |2(3)-5(1)| & |2(3)-5(2)| & |2(3)-5(3)| bmatrix = bmatrix 3 & 8 & 13 1 & 6 & 11 1 & 4 & 9 bmatrix The determinant of matrix A is: |A| = 3(54 - 44) - 8(9 - 11) + 13(4 - 6) |A| = 3(10) - 8(-2) + 13(-2) = 30 + 16 - 26 = 20 The element in the 2^ nd row and 3^ rd column of A⁻¹ is given by C₃₂ |A| , where C₃₂ is the cofactor of the element a₃₂ in matrix A . Calcula