The inverse of the matrix A = bmatrix 2 & -1 & 4 4 & -3 & 1 1 & 2 & 1 bmatrix is B = 1 37 bmatrix -5 & 9 & 11 -3 & -2 & 14 11 & -5 & k bmatrix , then the value of k is...

Step-by-step solution

Since B is the inverse of A , we have AB = I , which implies A(37B) = 37I . The element in the first row and third column of the matrix 37I is 0 . Multiplying the first row of A with the third column of 37B , we get: 2(11) + (-1)(14) + 4(k) = 0 22 - 14 + 4k = 0 8 + 4k = 0 k = -2 Alternatively, multiplying the third row of A with the third column of 37B gives the element in the third row and third column of 37I , which is 37 : 1(11) + 2(14) + 1(k) = 37 11 + 28 + k = 37 39 + k = 37 k = -2 Answer: -2