The given expression involves evaluating the following matrix operation:

$-3 \begin{bmatrix} 0 & -2 \\ 6 & 3 \end{bmatrix} + \begin{bmatrix} -8 & 2 \\ 7 & 1 \end{bmatrix} - 2 \begin{bmatrix} 5 & -5 \\ 6 & -9 \end{bmatrix}.$

Step 1: Simplify each term individually

1. Multiply $-3$ with the first matrix:

$-3 \begin{bmatrix} 0 & -2 \\ 6 & 3 \end{bmatrix} = \begin{bmatrix} -3 \cdot 0 & -3 \cdot (-2) \\ -3 \cdot 6 & -3 \cdot 3 \end{bmatrix} = \begin{bmatrix} 0 & 6 \\ -18 & -9 \end{bmatrix}.$

2. Leave the second matrix as it is:

$\begin{bmatrix} -8 & 2 \\ 7 & 1 \end{bmatrix}.$

3. Multiply $-2$ with the third matrix:

$-2 \begin{bmatrix} 5 & -5 \\ 6 & -9 \end{bmatrix} = \begin{bmatrix} -2 \cdot 5 & -2 \cdot (-5) \\ -2 \cdot 6 & -2 \cdot (-9) \end{bmatrix} = \begin{bmatrix} -10 & 10 \\ -12 & 18 \end{bmatrix}.$

Step 2: Add/Subtract the resulting matrices

Now combine the matrices: $\begin{bmatrix} 0 & 6 \\ -18 & -9 \end{bmatrix} + \begin{bmatrix} -8 & 2 \\ 7 & 1 \end{bmatrix} - \begin{bmatrix} -10 & 10 \\ -12 & 18 \end{bmatrix}.$

1. Add the first two matrices:

$\begin{bmatrix} 0 & 6 \\ -18 & -9 \end{bmatrix} + \begin{bmatrix} -8 & 2 \\ 7 & 1 \end{bmatrix} = \begin{bmatrix} 0 + (-8) & 6 + 2 \\ -18 + 7 & -9 + 1 \end{bmatrix} = \begin{bmatrix} -8 & 8 \\ -11 & -8 \end{bmatrix}.$

2. Subtract the third matrix:

$\begin{bmatrix} -8 & 8 \\ -11 & -8 \end{bmatrix} - \begin{bmatrix} -10 & 10 \\ -12 & 18 \end{bmatrix} = \begin{bmatrix} -8 - (-10) & 8 - 10 \\ -11 - (-12) & -8 - 18 \end{bmatrix}.$

Perform the operations element-wise: $\begin{bmatrix} -8 + 10 & 8 - 10 \\ -11 + 12 & -8 - 18 \end{bmatrix} = \begin{bmatrix} 2 & -2 \\ 1 & -26 \end{bmatrix}.$

Final Answer:

The result of the matrix expression is: $\boxed{\begin{bmatrix} 2 & -2 \\ 1 & -26 \end{bmatrix}}$

Do you want me to go over any specific steps or provide further explanations?

Here are five related questions you might find helpful:

1. What are some general rules for matrix addition and subtraction?
2. How does scalar multiplication work with matrices?
3. Can matrices of different dimensions be added or subtracted? Why or why not?
4. How is matrix multiplication different from scalar multiplication?
5. How are matrices used to solve systems of linear equations?

Tip: Always check the dimensions of matrices before performing operations to ensure compatibility.