Thanks for the video! It was truly well done!\n\nJust a point of clarification: shouldn't the column vector containing the biases at 14:40 be indexed from 0 to k (rather than 0 to n), since you're supposing there are (k+1) neurons in the first hidden layer after the input layer, and hence (k+1) biases? You need the same dimensionality to sum the matrix product and the *b* vector anyhow. And at 16:00 it seems the *a^(0)* matrix changed from its correct form at 14:40. It should have dimension (k+1)x(n) as it did at 14:40, but the k and n indices have been interchanged. Thanks again and I'm looking forward to the next video!