This image contains a matrix problem. The problem provides two matrices A and B, and asks for the result of the expression $3A + 2B$. Let's first break down the given matrices and perform the necessary calculations.

Given: $A = \begin{bmatrix} 4 & -1 \\ 3 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} -3 & -2 \\ 1 & 5 \end{bmatrix}$

We need to calculate $3A + 2B$.

Step 1: Multiply matrix A by 3:

$3A = 3 \times \begin{bmatrix} 4 & -1 \\ 3 & 2 \end{bmatrix} = \begin{bmatrix} 12 & -3 \\ 9 & 6 \end{bmatrix}$

Step 2: Multiply matrix B by 2:

$2B = 2 \times \begin{bmatrix} -3 & -2 \\ 1 & 5 \end{bmatrix} = \begin{bmatrix} -6 & -4 \\ 2 & 10 \end{bmatrix}$

Step 3: Add $3A$ and $2B$:

$3A + 2B = \begin{bmatrix} 12 & -3 \\ 9 & 6 \end{bmatrix} + \begin{bmatrix} -6 & -4 \\ 2 & 10 \end{bmatrix}$ $= \begin{bmatrix} 12 + (-6) & -3 + (-4) \\ 9 + 2 & 6 + 10 \end{bmatrix} = \begin{bmatrix} 6 & -7 \\ 11 & 16 \end{bmatrix}$

So, the result of $3A + 2B$ is: $\begin{bmatrix} 6 & -7 \\ 11 & 16 \end{bmatrix}$

The correct answer corresponds to option e.

Would you like more details on this solution or have any questions?

Here are some related questions:

1. How do you multiply matrices by a scalar?
2. How do you add matrices together?
3. What is the concept of matrix operations?
4. Can matrix multiplication and scalar multiplication be combined?
5. How do you verify matrix results for correctness?

Tip: Always check if the dimensions of matrices match before performing operations like addition or subtraction.