To solve the given problem $2A - B$, let us break it down step by step.

Given Matrices:

$A = \begin{pmatrix} 2 & 4 \\ 3 & 9 \end{pmatrix}, \quad B = \begin{pmatrix} -3 & -9 \\ -2 & -4 \end{pmatrix}$

We need to calculate: $2A - B$

Step 1: Calculate $2A$

Multiply each element of $A$ by 2: $2A = 2 \cdot \begin{pmatrix} 2 & 4 \\ 3 & 9 \end{pmatrix} = \begin{pmatrix} 4 & 8 \\ 6 & 18 \end{pmatrix}$

Step 2: Calculate $2A - B$

Subtract $B$ from $2A$: $2A - B = \begin{pmatrix} 4 & 8 \\ 6 & 18 \end{pmatrix} - \begin{pmatrix} -3 & -9 \\ -2 & -4 \end{pmatrix}$

Perform element-wise subtraction: $2A - B = \begin{pmatrix} 4 - (-3) & 8 - (-9) \\ 6 - (-2) & 18 - (-4) \end{pmatrix}$ $2A - B = \begin{pmatrix} 4 + 3 & 8 + 9 \\ 6 + 2 & 18 + 4 \end{pmatrix}$ $2A - B = \begin{pmatrix} 7 & 17 \\ 8 & 22 \end{pmatrix}$

Final Answer:

$\boxed{\begin{pmatrix} 7 & 17 \\ 8 & 22 \end{pmatrix}}$

This matches option 3.

Would you like me to provide additional details on the steps or explain matrix operations further?

Here are 5 related questions to expand your understanding:

1. What are the basic operations in matrix arithmetic?
2. How does scalar multiplication of a matrix work?
3. Can you calculate $A + B$ using the given matrices?
4. How do you determine if two matrices are equal?
5. What happens when you multiply two matrices together?

Tip: Always align matrices properly when performing subtraction or addition to avoid errors.