$\begin{array}{l}A=\left[\begin{array}{rrr}1 & -9 & -1 \\ -4 & -7 & -2\end{array}\right], B=\left[\begin{array}{rr}-7 & -8 \\ -5 & 1\end{array}\right], C=\left[\begin{array}{rrr}9 & -4 & -5 \\ 6 & 3 & 6 \\ 5 & 5 & -1\end{array}\right] \text {, and } D=\left[\begin{array}{rr}-5 & 3 \\ 1 & -2 \\ -3 & -8\end{array}\right] \\ B+A D\end{array}$

Step 1 ：Given matrices A, B, and D as follows: \(A = \left[\begin{array}{rrr}1 & -9 & -1 \\ -4 & -7 & -2\end{array}\right]\), \(B = \left[\begin{array}{rr}-7 & -8 \\ -5 & 1\end{array}\right]\), and \(D = \left[\begin{array}{rr}-5 & 3 \\ 1 & -2 \\ -3 & -8\end{array}\right]\).

Step 2 ：We are asked to find the result of the operation \(B + AD\).

Step 3 ：First, we calculate the product of matrices A and D. Matrix multiplication is done element by element, with the element in the i-th row and j-th column of the resulting matrix being the sum of the products of the corresponding elements in the i-th row of the first matrix and the j-th column of the second matrix. The result of \(AD\) is \(\left[\begin{array}{rr}-11 & 29 \\ 19 & 18\end{array}\right]\).

Step 4 ：Next, we add the resulting matrix to matrix B. Matrix addition is also done element by element, with the element in the i-th row and j-th column of the resulting matrix being the sum of the corresponding elements in the i-th row and j-th column of the two matrices being added. The result of \(B + AD\) is \(\left[\begin{array}{rr}-18 & 21 \\ 14 & 19\end{array}\right]\).

Step 5 ：Final Answer: The result of the operation \(B+AD\) is the matrix \(\boxed{\left[\begin{array}{rr}-18 & 21 \\ 14 & 19\end{array}\right]}\).