In [2]:

```
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
```

In [18]:

```
M = np.array([[0.7, 0.1, 0.3], [0.1, 0.8, 0.3], [0.2, 0.1, 0.4]])
print(M.round(2))
```

*democrats*, the second for *republicans*, the third for *independents*.

In [19]:

```
x = np.array([0.5, 0.5, 0.0])
```

In [21]:

```
for i in range(100):
x = M.dot(x)
print(x)
```

How do we know this converged? Does it depend on how it started?

In [ ]:

```
```