In the Linear Model lesson, you have taken the input vector is a row vector and the output vector is a column vector. Is any specific reason to do this? I mean to say, we can take the input vector as a column vector and output vector as a row vector.
You are trying to multiply the values in these vectors in a certain way to produce identical linear equations. In general, you can achieve that in more than one way, but your final way is to always get:
y = w0 + w1*x1 + w2*x2 + etc.