#!/usr/bin/env python
# coding: utf-8

# In[16]:


# D. Scott
# Linear Algebra: TCI
# Code Challenge 8.1
# Find null space vector and test commutativity

import random
import numpy as np
from scipy.linalg import null_space

# generate and populate random matrices with same inner value
num1 = []
num2 = []
for i in range(0,12):
    num1.append(random.randint(-6,12))
for i in range(0,12):
    num2.append(random.randint(-6,12))
A1 = np.array(num1).reshape(4,3)
A2 = np.array(num2).reshape(3,4)

A = A1@A2

num1 = []
num2 = []
for i in range(0,12):
    num1.append(random.randint(-6,12))
for i in range(0,12):
    num2.append(random.randint(-6,12))
B1 = np.array(num1).reshape(4,3)
B2 = np.array(num2).reshape(3,4)

B = B1@B2

print("A:\n",A,"\nRank(A): ",np.linalg.matrix_rank(A),
      "\n\nB:\n",B,"\nRank(B):",np.linalg.matrix_rank(B))

n = null_space(A)
print("\nBasis for N(A) [n]:\n",n)
print("\nB@A@n (zeros) = \n",B@A@n)
print("\nA@B@n = \n",A@B@n)
print("\nMatrix multiplication not commutative.")