W2_A2_How W[2]T.dZ[2] is a (n[1],m) matrix?

Course Q&A Deep Learning Specialization Neural Networks and Deep Learning
1

I was taking notes for the W2, Gradient Descent for Neural networks lecture and I’m still not able to understand how the matrix multiplication would result in a (n[1],m) matrix. Could someone guide me with this?

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Well, what are the dimensions of the objects in question?

W^{[2]} is n^{[2]} x n^{[1]}

and

dZ^{[2]} is n^{[2]} x m

So when you do the transpose, the dot product is:

n^{[1]} x n^{[2]} dotted with n^{[2]} x m

Which has the result n^{[1]} x m, right?

Of course you then do the elementwise multiply with g^{[1]'}(Z^{[1]}), but that works because the latter has the same shape as Z^{[1]}.

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