Find the following matrices where $A=\left[\begin{array}{rr}7 & -3 \\ -4 & -7 \\ 7 & -9\end{array}\right]$ and $B=\left[\begin{array}{rr}0 & 9 \\ -2 & -5 \\ -7 & 6\end{array}\right]$. a. $A+B$ b. $A-B$ c. $2 \mathrm{~A}$ d. $5 A-3 B$ a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. B. This matrix operation is not possible. b. Select the correct choice below and, if neceissary, fill in the answer box to complete your choice. A. $A-B=\square$ (Simplify your answer.) B. This matrix operation is not possible.

Step 1 ：Given matrices $A=\left[\begin{array}{rr}7 & -3 \ -4 & -7 \ 7 & -9\end{array}\right]$ and $B=\left[\begin{array}{rr}0 & 9 \ -2 & -5 \ -7 & 6\end{array}\right]$

Step 2 ：For matrix addition and subtraction, we perform the operations element-wise. That is, the element in the i-th row and j-th column of the resulting matrix is the sum or difference of the elements in the i-th row and j-th column of the original matrices.

Step 3 ：For scalar multiplication, we multiply each element of the matrix by the scalar.

Step 4 ：Performing these operations, we find:

Step 5 ：$A+B=\left[\begin{array}{rr}7 & 6 \ -6 & -12 \ 0 & -3\end{array}\right]$

Step 6 ：$A-B=\left[\begin{array}{rr}7 & -12 \ -2 & -2 \ 14 & -15\end{array}\right]$

Step 7 ：$2A=\left[\begin{array}{rr}14 & -6 \ -8 & -14 \ 14 & -18\end{array}\right]$

Step 8 ：For the operation $5A-3B$, we first multiply each matrix by its respective scalar, then subtract the two resulting matrices element-wise.

Step 9 ：Performing this operation, we find $5A-3B=\left[\begin{array}{rr}35 & -42 \ -14 & -20 \ 56 & -63\end{array}\right]$

Step 10 ：Thus, the final answers are \(\boxed{A+B=\left[\begin{array}{rr}7 & 6 \ -6 & -12 \ 0 & -3\end{array}\right]}\), \(\boxed{A-B=\left[\begin{array}{rr}7 & -12 \ -2 & -2 \ 14 & -15\end{array}\right]}\), \(\boxed{2A=\left[\begin{array}{rr}14 & -6 \ -8 & -14 \ 14 & -18\end{array}\right]}\), and \(\boxed{5A-3B=\left[\begin{array}{rr}35 & -42 \ -14 & -20 \ 56 & -63\end{array}\right]}\)