```python
import math
import numpy as np
from sympy import Matrix
```


```python
a = [[2,-1,1],[1,0,1],[3,-1,4]]
```


```python
mtx = Matrix(a)
```


```python
mtx
```




$\displaystyle \left[\begin{matrix}2 & -1 & 1\\1 & 0 & 1\\3 & -1 & 4\end{matrix}\right]$




```python
inv_mtx = mtx.inv()
```


```python
inv_mtx
```




$\displaystyle \left[\begin{matrix}\frac{1}{2} & \frac{3}{2} & - \frac{1}{2}\\- \frac{1}{2} & \frac{5}{2} & - \frac{1}{2}\\- \frac{1}{2} & - \frac{1}{2} & \frac{1}{2}\end{matrix}\right]$




```python
mtx_norm = np.linalg.norm(mtx, ord=math.inf)
```


```python
inv_mtx_norm = np.linalg.norm(inv_mtx, ord=math.inf)
```


```python
mtx_norm
```




$\displaystyle 8$




```python
inv_mtx_norm
```




$\displaystyle \frac{7}{2}$




```python
condition_number = mtx_norm * inv_mtx_norm
```


```python
condition_number
```




$\displaystyle 28$



The linear system is conditioned


```python

```

6f5c6f95623fd0e85adce4979db0db8337c46786
ipynb
Jupyter Notebook
condition_number.ipynb
lgtejas/mfds
dc9569a970f963d298dbe56db58b090684558d7b
MIT
condition_number.ipynb
lgtejas/mfds
dc9569a970f963d298dbe56db58b090684558d7b
MIT
condition_number.ipynb
lgtejas/mfds
dc9569a970f963d298dbe56db58b090684558d7b
MIT
Qwen/Qwen-72B
1. YES
2. YES