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Let's solve the problem step by step.

You are asked to find the element \( a_{22} \) (the element in the second row and second column) from the matrix \( 2A - 3B \).

### Given matrices:
\[
A = \begin{pmatrix} 1 & -2 & -6 \\ -2 & 1 & -3 \end{pmatrix}
\]
\[
B = \begin{pmatrix} 2 & 8 & -5 \\ 4 & -2 & 7 \end{pmatrix}
\]

### Step 1: Multiply matrix \( A \) by 2
\[
2A = 2 \times \begin{pmatrix} 1 & -2 & -6 \\ -2 & 1 & -3 \end{pmatrix}
= \begin{pmatrix} 2 & -4 & -12 \\ -4 & 2 & -6 \end{pmatrix}
\]

### Step 2: Multiply matrix \( B \) by 3
\[
3B = 3 \times \begin{pmatrix} 2 & 8 & -5 \\ 4 & -2 & 7 \end{pmatrix}
= \begin{pmatrix} 6 & 24 & -15 \\ 12 & -6 & 21 \end{pmatrix}
\]

### Step 3: Subtract \( 3B \) from \( 2A \)
\[
2A - 3B = \begin{pmatrix} 2 & -4 & -12 \\ -4 & 2 & -6 \end{pmatrix}
- \begin{pmatrix} 6 & 24 & -15 \\ 12 & -6 & 21 \end{pmatrix}
= \begin{pmatrix} 2 - 6 & -4 - 24 & -12 + 15 \\ -4 - 12 & 2 + 6 & -6 - 21 \end{pmatrix}
= \begin{pmatrix} -4 & -28 & 3 \\ -16 & 8 & -27 \end{pmatrix}
\]

### Step 4: Identify the element \( a_{22} \) from \( 2A - 3B \)
The element in the second row and second column is \( a_{22} = 8 \).

### Final Answer:
The correct choice is **d. 8**.

Would you like further explanation or details on any part of this process?

### Related Questions:
1. What is the element \( a_{12} \) from the matrix \( 2A - 3B \)?
2. How do you perform matrix addition and subtraction?
3. What is the result of multiplying a matrix by a scalar?
4. Can the subtraction of matrices be performed if the dimensions are not the same?
5. What are some real-life applications of matrix operations?

### Tip:
When multiplying matrices by scalars or subtracting matrices, ensure the operations are element-wise.

What element is in a_{22} when 2A - 3B is evaluated? Matrices provided: A = ((1, -2, -6), (-2, 1, -3)) and B = ((2, 8, -5), (4, -2, 7))

Learn how to evaluate the element in position a_{22} from the matrix 2A - 3B. This involves multiplying matrices by scalars and performing matrix subtraction. Suitable for high school students studying algebra and linear algebra.

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