Create three lists $($A$,$ B$,$ and C$)$ with random values in Python such that each list contains five real values. Calculate the distances between the lists using the formulas below.

$d(A,B)=\sqrt[\phantom{2}]{{\displaystyle \underset{i=1}{\overset{5}{}}}(A_i-B_i{)}^2}$

$d(A,B)=\sqrt[\phantom{2}]{(A_i-B_i{)}^T(A_i-B_i)}$

cosine$(A,B)=\frac{A*B}{|A||B|}$

Here, $({)}^T$ is transpose. $(.)$ denotes dot product and $||$ presents the magnitude of the vector. You MUST implement these equations from scratch without using any Python library or routines.

Randomly generate two matrices $($P and Q$)$ with four rows and five columns. You can use numpy arrays in Python. Write a program that obtains L$(2,1)-$norm of a matrix. First, take the L$2$ norm of each row of a matrix as below.

$P_{\text{r}\text{n}\text{o}\text{r}\text{m}}(i)=\sqrt[\phantom{2}]{{\displaystyle \underset{j}{\overset{n_{\text{c}\text{o}\text{l}}}{}}}{P}_{ij}^2}$

This is actually sum of squared values in each row. Then, obtain the L$1$ norm of the L$2$ norm values $P_{\text{r}\text{n}\text{o}\text{r}\text{m}}$ as below.

$P_{2,1}={\displaystyle \underset{i}{\overset{n_{\text{r}\text{o}\text{w}}}{}}}|P_{\text{r}\text{n}\text{o}\text{r}\text{m}}(i)|$

Here, $n_{\text{r}\text{o}\text{w}}$ and $n_{\text{c}\text{o}\text{l}}$ represent the numbers of rows and columns, respectively.