import numpy as np

A = np.array ( [ 
  [ 2, 1 ], 
  [ 3, 1 ], 
  [ 5, 1 ], 
  [ 7, 1 ],
  [ 9, 1 ] 
] )

y = np.array ( [ 4, 5, 7, 10, 15 ] )
#
#  Solve A*x=y for x in the least squares sense.
#
x, resid, rank, s = np.linalg.lstsq ( A, y, rcond = None )
print ( '  x = ', x )
y2 = A * x

print ( '  ||y|| = ', np.linalg.norm(y), ' ? <= ? ||A|| * ||x|| = ', np.linalg.norm (A), '*', np.linalg.norm(x), '=', np.linalg.norm(A)*np.linalg.norm(x) )

print ( '  ||y2|| = ', np.linalg.norm(y2), ' <= ||A|| * ||x|| = ', np.linalg.norm (A), '*', np.linalg.norm(x), '=', np.linalg.norm(A)*np.linalg.norm(x) )