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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.

If A = [2  1 ; 0  3] - [1  -1 ; 1  4] and B = [2  -1 ; -3  2], find: a) 3A + 2B, b) 7A - 4B

This problem involves matrix operations such as addition, scalar multiplication, and subtraction. Learn how to compute 3A + 2B and 7A - 4B with detailed steps, using matrix A = [2  1; 0  3] - [1  -1; 1  4] and B = [2  -1; -3  2].

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