# -*- coding: utf-8 -*-
"""
Created on Thu Sep 15 14:05:21 2022

@author: Chris
Lab 8 Q2
"""

import numpy as np
from scipy import linalg as la

A = np.random.rand(4,4)
a = np.array([[1,0,2,3]])

b = np.array([[1],[3],[-1],[2]])

print('A^T=')
print(A.T)
print('')

print('A b=')
print(A @ b)
print('')

AI = la.inv(A)
print('A^{-1}=')
print(AI)
print('')

print('Check:')
print(A @ AI)

print('L2 norm Difference from identity:')
print(la.norm(A @ AI - np.eye(len(A)),2))