<s>[INST] Given the following observation matrix A:
```
1 0 0 0 0 0 0 5 0
0 2 0 0 0 0 0 0 0
0 0 3 0 0 0 0 0 0
0 0 0 4 0 0 0 0 0
0 0 0 0 5 0 0 0 0
0 0 0 0 0 6 0 0 0
0 0 0 0 0 0 7 0 0
0 0 0 0 0 0 0 8 0
0 5 0 0 0 0 0 0 0
```
This matrix is diagonally dominant, and we want to use Gauss-Seidel method to find its eigenvalues.

However, if we want to use this method, we need to iteratively apply the matrix to an initial vector. For this problem, we will use the following initial vector:
```
[1, 1, 1, 1, 1, 1, 1, 1, 1]
```
However, applying the matrix to this initial vector, we get:
```
[6, 2, 3, 4, 5, 6, 7, 8, 5]
```
This does not match the first eigenvector of a diagonally dominant matrix, which should be close to the first column of the original matrix.
I'm a bit lost on what I'm doing wrong. My code is below:
```python
import numpy as np[/INST]