Serious mistake when you multiplicate a vector by a matrix

Good morning. As already said by other students, I want to report that around minute 2:30 you do a wrong multiplication: I think that you wanted to show the transposed of the 2x2 matrix you show, and not that one. In fact, when you multiply a 1xa vector by a axb matrix, you should know that the k-th element of the output vector is given by the first row of the initial vector (that is the initial vector itself) multiplied by the k-th column of the matrix.
Furthermore, around minute 3:30 it's a bit confusing to show a bias vector of 1xM: it should be an NxM matrix to be consistent with the other addends, unless by B_i you meant a column vector with dimension N (that is a bit confusing, though)
Thanks