Matrix shapes difference between lectures
Both ways are fine, it only matters to be consistent, i.e., that all matrix operations are correct. Depending on the shape of the matrix you might have matrix*vector or vector_transposed*matrix, or some variety along these lines.
Playing around with different representations might actually help the understanding in the long run. So I would recommend to follow both lectures and appreciate the differences in how they represent the data etc.
I'm currently learning deep-learning from two lectures. What gets me confused is that there is a notation difference between two lectures when they shape an input matrix X. 
In Coursera's lecture, they make a matrix X in shape of (number of features, number of samples), so that they stack the samples vertically. Otherwise, the other lecture stacks the samples horizontally, so that every row represents one sample.
What makes this difference and which one should I follow?