This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The 18 came from two steps in the calculation for part a) (ii): 1. Substituting x = -2 into the original matrix K: The original matrix was K = 8 & 9x \\ 1 & x . In part a) (i), we found x = -2. When we substitute x = -2 into the element 9x, we get: 9x = 9(-2) = -18 So, the matrix K became: K = 8 & -18 \\ 1 & -2 2. Applying the inverse formula: For a matrix a & b \\ c & d , the inverse is (1)/((K)) d & -b \\ -c & a . From our matrix K = 8 & -18 \\ 1 & -2 , we have b = -18. Therefore, the -b term in the inverse formula becomes: -b = -(-18) = 18 This is why the adjoint matrix was -2 & 18 \\ -1 & 8 . Finally, this 18 was divided by the determinant (which was 2) to get 9 in the final inverse matrix. That's 2 down. 3 left today — send the next one.