🧮 Why does NumPy let you add a number to an entire matrix?

Look at this:

import numpy as np

x = np.array([
    [10, 20, 30],
    [40, 50, 60]
])

x + 5

You get:

[[15, 25, 35],
 [45, 55, 65]]

But where did the 5 go? You didn't write a loop. You didn't copy 5 six times.

This is broadcasting.
NumPy automatically treats the smaller object as if it were expanded to match the larger array's shape.

So conceptually:

[[10, 20, 30],       [[5, 5, 5],
 [40, 50, 60]]   +    [5, 5, 5]]

Then it adds them element by element.

And it works with arrays too:

x + np.array([1, 2, 3])

Conceptually:

[[10, 20, 30],       [[1, 2, 3],
 [40, 50, 60]]   +    [1, 2, 3]]

Result:

[[11, 22, 33],
 [41, 52, 63]]

The important part:
Broadcasting doesn't literally copy the data into a bigger array.
NumPy applies the operation as if the smaller array had been expanded, while avoiding unnecessary copies.

That's why this:

x + 5

can work even though x is 2D and 5 is just a scalar.