The element in the third row and the second column in the inverse matrix of a matrix bmatrix 1 & 3 & 3 3 & 1 & 3 3 & 3 & 4 bmatrix is

Step-by-step solution

Let A = bmatrix 1 & 3 & 3 3 & 1 & 3 3 & 3 & 4 bmatrix . The element in the third row and second column of A⁻¹ is given by C₂₃ |A| , where C₂₃ is the cofactor of the element a₂₃ in A . First, we calculate the determinant of A : |A| = 1(1 4 - 3 3) - 3(3 4 - 3 3) + 3(3 3 - 1 3) |A| = 1(-5) - 3(3) + 3(6) = -5 - 9 + 18 = 4 Next, we find the cofactor C₂₃ : C₂₃ = (-1)²⁺³ vmatrix 1 & 3 3 & 3 vmatrix = -(1 3 - 3 3) = -(3 - 9) = 6 Therefore, the required element is C₂₃ |A| = 6 4 = 3 2 . Answer: 3 2