```python
from sympy import symbols, Matrix
```


```python
a, b, c, d = symbols('a b c d')
Yt_1, Yt_2, Gt_1 = symbols('Yt_1 Yt_2 Gt_1')
C, I, G, Yt = symbols('C I G Yt')
Yt_1, Yt_2, Gt_1 = symbols('Yt_1 Yt_2 Gt_1')
e, u, v = symbols('e u v')

```


```python
A = Matrix([
    [1, 0, 0, 0],
    [0, 1, 0, 0],
    [0, 0, 1, 0],
    [-1, -1, -1, 1]
])
```


```python
B = Matrix([
    [-b, -a, 0, 0],
    [0, -c, c, 0],
    [0, 0, 0, -d],
    [0, 0, 0, 0]
])
```


```python
Y = Matrix([
    [C],
    [I],
    [G],
    [Yt]
])
```


```python
X = Matrix([
    [1],
    [Yt_1],
    [Yt_2],
    [Gt_1]
])
```


```python
U = Matrix([
    [e],
    [u],
    [v],
    [0]
])
```


```python
# Y = M*X + A.inv() * U
```


```python
Y
```




$\displaystyle \left[\begin{matrix}C\\I\\G\\Yt\end{matrix}\right]$




```python
M = -A.inv() * B
M
```




$\displaystyle \left[\begin{matrix}b & a & 0 & 0\\0 & c & - c & 0\\0 & 0 & 0 & d\\b & a + c & - c & d\end{matrix}\right]$




```python
X
```




$\displaystyle \left[\begin{matrix}1\\Yt_{1}\\Yt_{2}\\Gt_{1}\end{matrix}\right]$




```python
A.inv()
```




$\displaystyle \left[\begin{matrix}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\1 & 1 & 1 & 1\end{matrix}\right]$




```python
U
```




$\displaystyle \left[\begin{matrix}e\\u\\v\\0\end{matrix}\right]$




```python

```


```python

```

9a437aba9aa3c53caf5be8a5cc6b12fab32eda36
ipynb
Jupyter Notebook
Course III/ECONOMETRICS/solver.ipynb
GeorgiyDemo/FA
641a29d088904302f5f2164c9b3e1f1c813849ec
WTFPL
2019-08-18T20:54:27.000Z
2022-02-22T02:39:45.000Z
Course III/ECONOMETRICS/solver.ipynb
GeorgiyDemo/FA
641a29d088904302f5f2164c9b3e1f1c813849ec
WTFPL
2019-09-22T14:43:25.000Z
2022-03-30T13:49:18.000Z
Course III/ECONOMETRICS/solver.ipynb
GeorgiyDemo/FA
641a29d088904302f5f2164c9b3e1f1c813849ec
WTFPL
2019-09-18T11:36:28.000Z
2022-03-19T18:43:00.000Z
Qwen/Qwen-72B
1. YES
2. YES