```python
from sympy import *
from sympy.abc import *
Matrix([x,y,z])
```




$\displaystyle \left[\begin{matrix}x\\y\\z\end{matrix}\right]$




```python
e1 = 5*x+3*y+4*z
e2 = 3*x+4*y+5*z
e3 = 4*x+5*y+3*z
```


```python
A = Matrix([e1,e2,e3])
A
```




$\displaystyle \left[\begin{matrix}5 x + 3 y + 4 z\\3 x + 4 y + 5 z\\4 x + 5 y + 3 z\end{matrix}\right]$




```python
B = A*2
B
```




$\displaystyle \left[\begin{matrix}10 x + 6 y + 8 z\\6 x + 8 y + 10 z\\8 x + 10 y + 6 z\end{matrix}\right]$




```python
Integral(A,x)
```




$\displaystyle \int \left[\begin{matrix}5 x + 3 y + 4 z\\3 x + 4 y + 5 z\\4 x + 5 y + 3 z\end{matrix}\right]\, dx$




```python
Integral(A,x).doit()
```




$\displaystyle \left[\begin{matrix}\frac{5 x^{2}}{2} + x \left(3 y + 4 z\right)\\\frac{3 x^{2}}{2} + x \left(4 y + 5 z\right)\\2 x^{2} + x \left(5 y + 3 z\right)\end{matrix}\right]$




```python
Derivative(A,x)
```




$\displaystyle \frac{\partial}{\partial x} \left[\begin{matrix}5 x + 3 y + 4 z\\3 x + 4 y + 5 z\\4 x + 5 y + 3 z\end{matrix}\right]$




```python
Derivative(A,x).doit()
```




$\displaystyle \left[\begin{matrix}5\\3\\4\end{matrix}\right]$



1b7a8e2ed4d2e50a59795314ec97d1b86ebc8b15
ipynb
Jupyter Notebook
Personal_Projects/Matrix_Calculus.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Personal_Projects/Matrix_Calculus.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Personal_Projects/Matrix_Calculus.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Qwen/Qwen-72B
1. YES
2. YES