Hello,
I see Andrew-Ng showed how we could use the vectorization vector to calculate Z,A, dw e.t.c. without using loop. I got that but I didn’t get why J was not calculated when Logistic Regression was calculated using a vectorization vector as shown in the attached image.

You will be asked to figure out how to compute J in the second assignment of the Week 2, and it suggests you to use np.dot for doing it vectorized-wise.

For the update formula, I suggest you to watch the Course 1 Week 2 Video: Gradient Descent where they are introduced and explained, and let us know what you have got if you still have questions about that.