The problem asks to compute $5A - 5B$ where $A$ and $B$ are given matrices:

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

Step 1: Multiply matrix $A$ and $B$ by 5

First, we'll compute $5A$ and $5B$ by multiplying each element of $A$ and $B$ by 5.

$5A = 5 \times \begin{bmatrix} 1 & 3 \\ -2 & 5 \\ 2 & 4 \end{bmatrix} = \begin{bmatrix} 5 & 15 \\ -10 & 25 \\ 10 & 20 \end{bmatrix}$ $5B = 5 \times \begin{bmatrix} 2 & -1 \\ 4 & 1 \\ -1 & -5 \end{bmatrix} = \begin{bmatrix} 10 & -5 \\ 20 & 5 \\ -5 & -25 \end{bmatrix}$

Step 2: Subtract $5B$ from $5A$

Now, subtract $5B$ from $5A$:

$5A - 5B = \begin{bmatrix} 5 & 15 \\ -10 & 25 \\ 10 & 20 \end{bmatrix} - \begin{bmatrix} 10 & -5 \\ 20 & 5 \\ -5 & -25 \end{bmatrix}$

This results in:

$5A - 5B = \begin{bmatrix} 5 - 10 & 15 - (-5) \\ -10 - 20 & 25 - 5 \\ 10 - (-5) & 20 - (-25) \end{bmatrix} = \begin{bmatrix} -5 & 20 \\ -30 & 20 \\ 15 & 45 \end{bmatrix}$

Final Answer:

$5A - 5B = \begin{bmatrix} -5 & 20 \\ -30 & 20 \\ 15 & 45 \end{bmatrix}$

Would you like a detailed explanation of any step?

Here are 5 questions related to the topic:

1. How do you perform scalar multiplication on a matrix?
2. What is matrix addition and subtraction?
3. What is the determinant of a matrix, and how is it calculated?
4. How can matrices be used to solve systems of linear equations?
5. What are the properties of matrix multiplication?

Tip: Always verify the dimensions of matrices when performing operations like addition or multiplication to ensure they are compatible.