When you use the + operator with a NumPy array and a tuple, NumPy implicitly converts the tuple into an ndarray and then applies its broadcasting rules. In your example, instead of adding b (which is a NumPy array) to a, you inadvertently add the tuple b.shape (i.e. (3,)) to a.

Here's what typically happens,

When you do a + b.shape, NumPy internally converts the tuple (3,) to an ndarray using something similar to np.asarray(b.shape). This gives you an array with a single element, effectively array().

The resulting array is broadcast to match the shape of a (which is (4,3)). The broadcasting process treats array() as if it had shape (1,1), so it is expanded to (4,3), and every element in a gets 3 added to it.

Finally, This is why you observe that each element in a increases by 3, resulting in an array where every entry is a[i][j] + 3.

Pretty much, NumPy's ufunc mechanism automatically handles non-ndarray operands by converting them and applying its standard broadcasting rules.