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The task is to compute \( 2B - 3A \), where matrices \( A \) and \( B \) are given as:

\[
A = \begin{pmatrix} 
2 & -1 \\
6 & 10 \\
7 & -10 
\end{pmatrix}, \quad
B = \begin{pmatrix} 
-1 & -3 & -10 \\
10 & -2 & 0 
\end{pmatrix}
\]

Let's break this down step by step:

### Step 1: Compute \( 2B \)
We multiply matrix \( B \) by 2:
\[
2B = 2 \times \begin{pmatrix} 
-1 & -3 & -10 \\
10 & -2 & 0 
\end{pmatrix}
= \begin{pmatrix} 
2 \times (-1) & 2 \times (-3) & 2 \times (-10) \\
2 \times 10 & 2 \times (-2) & 2 \times 0 
\end{pmatrix}
= \begin{pmatrix} 
-2 & -6 & -20 \\
20 & -4 & 0 
\end{pmatrix}
\]

### Step 2: Compute \( 3A \)
Next, multiply matrix \( A \) by 3:
\[
3A = 3 \times \begin{pmatrix} 
2 & -1 \\
6 & 10 \\
7 & -10 
\end{pmatrix}
= \begin{pmatrix} 
3 \times 2 & 3 \times (-1) \\
3 \times 6 & 3 \times 10 \\
3 \times 7 & 3 \times (-10) 
\end{pmatrix}
= \begin{pmatrix} 
6 & -3 \\
18 & 30 \\
21 & -30
\end{pmatrix}
\]

### Step 3: Subtract \( 3A \) from \( 2B \)
Since matrix \( 2B \) is \( 2 \times 3 \) and matrix \( 3A \) is \( 3 \times 2 \), these two matrices have different dimensions. You can only add or subtract matrices if they have the same dimensions, so:

**Answer: "Not Possible"**

Would you like further clarification on any step? Here are some related questions to deepen your understanding:

1. What are the conditions for matrix addition and subtraction?
2. How do you multiply a scalar with a matrix?
3. What are the different matrix dimensions and their implications?
4. How do you determine when two matrices are conformable for addition or subtraction?
5. What are some real-world applications of matrix operations?

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

Given the following matrices, if possible, determine 2B - 3A. If not, state 'Not Possible'. A = [2, -1; 6, 10; 7, -10], B = [-1, -3, -10; 10, -2, 0].

Solve a matrix subtraction problem where A and B have different dimensions. Explore scalar multiplication, subtraction rules, and learn why 2B - 3A is 'Not Possible' when matrix dimensions don't match. Suitable for Grade 10-12 or college-level students.

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