Question: Given the following matrices, perform the indicated operation, if possible. A = [ 9 -2 -1 -8 0 -3 ], B = [ 1 0 -7 8 ], C = [ 3 3 -2 7 2 -2 -6 -8 2 ], and D = [ -6 8 -3 1 6 -7 ] B + AD Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. B + AD = B. The matrix product is not defined.

1. **State the problem:** We need to find the matrix sum $$B + AD$$ if it is defined. 2. **Check dimensions:** - Matrix $$A$$ is $$2 \times 3$$. - Matrix $$D$$ is $$3 \times 2$$. - Matrix $$B$$ is $$2 \times 2$$. 3. **Matrix multiplication feasibility:** - The product $$AD$$ is defined if the number of columns of $$A$$ equals the number of rows of $$D$$. - $$A$$ has 3 columns, $$D$$ has 3 rows, so $$AD$$ is defined. - The resulting matrix $$AD$$ will be $$2 \times 2$$. 4. **Calculate $$AD$$:** $$ AD = \begin{bmatrix}9 & -2 & -1 \\ -8 & 0 & -3\end{bmatrix} \times \begin{bmatrix}-6 & 8 \\ -3 & 1 \\ 6 & -7\end{bmatrix} $$ Calculate each element: - First row, first column: $$9 \times (-6) + (-2) \times (-3) + (-1) \times 6 = -54 + 6 - 6 = -54$$ - First row, second column: $$9 \times 8 + (-2) \times 1 + (-1) \times (-7) = 72 - 2 + 7 = 77$$ - Second row, first column: $$-8 \times (-6) + 0 \times (-3) + (-3) \times 6 = 48 + 0 - 18 = 30$$ - Second row, second column: $$-8 \times 8 + 0 \times 1 + (-3) \times (-7) = -64 + 0 + 21 = -43$$ So, $$ AD = \begin{bmatrix}-54 & 77 \\ 30 & -43\end{bmatrix} $$ 5. **Add $$B + AD$$:** $$ B = \begin{bmatrix}1 & 0 \\ -7 & 8\end{bmatrix} $$ Add element-wise: - Top-left: $$1 + (-54) = -53$$ - Top-right: $$0 + 77 = 77$$ - Bottom-left: $$-7 + 30 = 23$$ - Bottom-right: $$8 + (-43) = -35$$ So, $$ B + AD = \begin{bmatrix}-53 & 77 \\ 23 & -35\end{bmatrix} $$ 6. **Conclusion:** The matrix product $$AD$$ is defined and the sum $$B + AD$$ is: $$ \boxed{\begin{bmatrix}-53 & 77 \\ 23 & -35\end{bmatrix}} $$