You can multiply numpy arrays by scalars and it just works.
>>> import numpy as np
>>> np.array([1, 2, 3]) * 2
array([2, 4, 6])
>>> np.array([[1, 2, 3], [4, 5, 6]]) * 2
array([[ 2, 4, 6],
[ 8, 10, 12]])
This is also a very fast and efficient operation. With your example:
>>> a_1 = np.array([1.0, 2.0, 3.0])
>>> a_2 = np.array([[1., 2.], [3., 4.]])
>>> b = 2.0
>>> a_1 * b
array([2., 4., 6.])
>>> a_2 * b
array([[2., 4.],
[6., 8.]])