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To solve this, let's analyze the question.

We have two matrices \( A \) and \( B \):
\[
A = \begin{bmatrix} 4 & 1 & 2 \\ 7 & 5 & 8 \\ 9 & 1 & 3 \end{bmatrix} 
\quad \text{and} \quad 
B = \begin{bmatrix} -1 & -4 & 2 \\ 3 & 5 & 0 \\ 2 & 3 & 0 \end{bmatrix}.
\]

The question provides different statements, and we need to determine which one is true. Each statement likely involves matrix properties or operations such as matrix addition, subtraction, or scalar multiplication.

Let's analyze each option by determining if it might be true for matrices \( A \) and \( B \). 

I'll examine the options and give you a detailed answer shortly.Let's break down the options given to understand which one might be true for the matrices \( A \) and \( B \).

### Step 1: Understanding the Statements
The options seem to have the following format:
1. \( 5A - 2B = \text{Some Matrix} \)
2. Each option represents a matrix, and we must evaluate the expression \( 5A - 2B \) to see which one matches the options.

### Step 2: Calculating \( 5A \) and \( -2B \)
#### Matrix \( A \):
\[
A = \begin{bmatrix} 4 & 1 & 2 \\ 7 & 5 & 8 \\ 9 & 1 & 3 \end{bmatrix}
\]
Multiply \( A \) by 5:
\[
5A = \begin{bmatrix} 5 \cdot 4 & 5 \cdot 1 & 5 \cdot 2 \\ 5 \cdot 7 & 5 \cdot 5 & 5 \cdot 8 \\ 5 \cdot 9 & 5 \cdot 1 & 5 \cdot 3 \end{bmatrix} = \begin{bmatrix} 20 & 5 & 10 \\ 35 & 25 & 40 \\ 45 & 5 & 15 \end{bmatrix}
\]

#### Matrix \( B \):
\[
B = \begin{bmatrix} -1 & -4 & 2 \\ 3 & 5 & 0 \\ 2 & 3 & 0 \end{bmatrix}
\]
Multiply \( B \) by -2:
\[
-2B = \begin{bmatrix} -2 \cdot -1 & -2 \cdot -4 & -2 \cdot 2 \\ -2 \cdot 3 & -2 \cdot 5 & -2 \cdot 0 \\ -2 \cdot 2 & -2 \cdot 3 & -2 \cdot 0 \end{bmatrix} = \begin{bmatrix} 2 & 8 & -4 \\ -6 & -10 & 0 \\ -4 & -6 & 0 \end{bmatrix}
\]

### Step 3: Adding \( 5A \) and \( -2B \)
\[
5A - 2B = \begin{bmatrix} 20 & 5 & 10 \\ 35 & 25 & 40 \\ 45 & 5 & 15 \end{bmatrix} + \begin{bmatrix} 2 & 8 & -4 \\ -6 & -10 & 0 \\ -4 & -6 & 0 \end{bmatrix} = \begin{bmatrix} 22 & 13 & 6 \\ 29 & 15 & 40 \\ 41 & -1 & 15 \end{bmatrix}
\]

### Step 4: Checking the Options
Now, let's compare \( 5A - 2B = \begin{bmatrix} 22 & 13 & 6 \\ 29 & 15 & 40 \\ 41 & -1 & 15 \end{bmatrix} \) with each option in the question to find a match.

Please refer to the options on your question sheet, and match this result with the provided choices to see which one is correct.

Would you like more details on any part of this calculation? 

### Further Questions
1. What are the properties of matrix multiplication and addition?
2. How does scalar multiplication affect each element in a matrix?
3. Can matrices with different dimensions be added or subtracted?
4. Why is matrix addition commutative, but matrix multiplication isn’t?
5. How do you verify equality between two matrices?

**Tip:** When performing matrix operations, double-check each element to ensure accuracy, as small errors can lead to incorrect results.

If \(A = \begin{bmatrix} 4 & 1 & 2 \\ 7 & 5 & 8 \\ 9 & 1 & 3 \end{bmatrix} \) and \(B = \begin{bmatrix} -1 & -4 & 2 \\ 3 & 5 & 0 \\ 2 & 3 & 0 \end{bmatrix} \), then which of the following is true?

Solve the matrix equation 5A - 2B for the given matrices A and B. This problem involves matrix scalar multiplication and addition and provides step-by-step calculations. Suitable for undergraduate students studying linear algebra.

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