Vectorised Neural Network Backprapogation

I've started the CS231n course and have been going through the proofs and derivations for backpropagation. These two papers by the lecturers are what I've been reading:

Reading both papers individually they both make sense, but when trying to link the concepts explained in both together, something doesn't make sense to me.

Paper 2 lists the loss w.r.t the inputs as: dL/dX = dL/dY*W_transpose where W is the weights matrix This follows on from the use of the chain rule where dL/dX = dL/dY * dY/dX

Paper 1 however, mentions in the first sections that dY/dX = W which is the weights matrix, but not transposed.

My question is, am I missing something here as to why one paper mentions W transposed and the other doesn't?