I use np.dot and an error is raised informing me of a problem of ‘shapes’ which are of the form (3, 1) and (3, 1). I do not understand why.
Dot product works for two matrices (n,m), (m,s) to create (n,s) matrix. In your case, you need to transpose either like np.dot(x, y.T)
Regarding a dot product, please see this tread.