The problem asks to find the matrices for $3A + 2B$ and $7A - 4B$, where matrices $A$ and $B$ are provided as:

$A = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix} - \begin{bmatrix} 1 & -1 \\ 1 & 4 \end{bmatrix}$ $B = \begin{bmatrix} 2 & -1 \\ -3 & 2 \end{bmatrix}$

We need to first compute matrix $A$ by subtracting the second matrix from the first, and then use the formulas $3A + 2B$ and $7A - 4B$.

Let me compute that for you.The solutions to the given problem are:

1. $3A + 2B = \begin{bmatrix} 7 & 4 \\ -9 & 1 \end{bmatrix}$
2. $7A - 4B = \begin{bmatrix} -1 & 18 \\ 5 & -15 \end{bmatrix}$

Would you like further details on the steps or have any questions?

Here are some related questions to consider:

1. How would you compute the determinant of matrix $A$?
2. What happens if you transpose matrices $A$ and $B$?
3. Can you find the inverse of matrix $A$, if it exists?
4. What would $3A - 2B$ look like?
5. How can you multiply matrix $A$ by matrix $B$?

Tip: When adding or subtracting matrices, ensure their dimensions match exactly to perform the operations correctly.