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To solve for \( 4A + 3B \), we need to first multiply matrices \( A \) and \( B \) by their respective scalar values and then add the resulting matrices.

Given:
\[
A = \begin{bmatrix} 6 & 4 \\ 8 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} -3 & 5 \\ 5 & -3 \end{bmatrix}
\]

### Step 1: Multiply matrix \( A \) by 4
\[
4A = 4 \times \begin{bmatrix} 6 & 4 \\ 8 & 4 \end{bmatrix} = \begin{bmatrix} 24 & 16 \\ 32 & 16 \end{bmatrix}
\]

### Step 2: Multiply matrix \( B \) by 3
\[
3B = 3 \times \begin{bmatrix} -3 & 5 \\ 5 & -3 \end{bmatrix} = \begin{bmatrix} -9 & 15 \\ 15 & -9 \end{bmatrix}
\]

### Step 3: Add the resulting matrices \( 4A \) and \( 3B \)
\[
4A + 3B = \begin{bmatrix} 24 & 16 \\ 32 & 16 \end{bmatrix} + \begin{bmatrix} -9 & 15 \\ 15 & -9 \end{bmatrix} = \begin{bmatrix} 15 & 31 \\ 47 & 7 \end{bmatrix}
\]

So, the final result is:
\[
4A + 3B = \begin{bmatrix} 15 & 31 \\ 47 & 7 \end{bmatrix}
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do scalar multiplication and matrix addition work in general?
2. Can you explain the properties of matrix addition and scalar multiplication?
3. What would happen if we swapped the order of the operations in this case?
4. How would we perform matrix multiplication with matrices \( A \) and \( B \)?
5. What are the conditions for two matrices to be added or multiplied?

**Tip:** Always ensure that the matrices you're adding have the same dimensions, otherwise, matrix addition is undefined.

Learn how to find the result of 4A + 3B by applying matrix scalar multiplication and addition. This solution walks through each step with given matrices A and B, showing calculations for each element. Ideal for high school students studying linear algebra.

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