Find the following matrices where $A=\left[\begin{array}{l}3 \\ 7 \\ 9\end{array}\right]$ and $B=\left[\begin{array}{r}6 \\ 9 \\ -2\end{array}\right]$
a. $A+B$
b. $A-B$
c. $-5 \mathrm{~A}$
d. $3 A+2 B$

Step 1 ：Given matrices A and B as $A=\left[\begin{array}{l}3 \\ 7 \\ 9\end{array}\right]$ and $B=\left[\begin{array}{r}6 \\ 9 \\ -2\end{array}\right]$

Step 2 ：For part a, we need to find $A+B$. This is done by adding the corresponding elements in the two matrices. So, $A+B = \left[\begin{array}{l}3+6 \\ 7+9 \\ 9+(-2)\end{array}\right] = \left[\begin{array}{l}9 \\ 16 \\ 7\end{array}\right]$

Step 3 ：For part b, we need to find $A-B$. This is done by subtracting the corresponding elements in the two matrices. So, $A-B = \left[\begin{array}{l}3-6 \\ 7-9 \\ 9-(-2)\end{array}\right] = \left[\begin{array}{l}-3 \\ -2 \\ 11\end{array}\right]$

Step 4 ：For part c, we need to find $-5A$. This is done by multiplying every element in matrix A by -5. So, $-5A = \left[\begin{array}{l}-5*3 \\ -5*7 \\ -5*9\end{array}\right] = \left[\begin{array}{l}-15 \\ -35 \\ -45\end{array}\right]$

Step 5 ：For part d, we need to find $3A+2B$. This is done by multiplying every element in matrix A by 3 and every element in matrix B by 2, and then adding the results. So, $3A+2B = \left[\begin{array}{l}3*3+2*6 \\ 3*7+2*9 \\ 3*9+2*(-2)\end{array}\right] = \left[\begin{array}{l}21 \\ 39 \\ 23\end{array}\right]$

Step 6 ：Final Answer: \(\boxed{A+B = \left[\begin{array}{l}9 \\ 16 \\ 7\end{array}\right]}\), \(\boxed{A-B = \left[\begin{array}{l}-3 \\ -2 \\ 11\end{array}\right]}\), \(\boxed{-5A = \left[\begin{array}{l}-15 \\ -35 \\ -45\end{array}\right]}\), \(\boxed{3A+2B = \left[\begin{array}{l}21 \\ 39 \\ 23\end{array}\right]}\)