$[4$ points$]$ Suppose X represents the data matrix $($samples along columns$)$ containing information about $100$ individuals

$($a$)$ Suppose we want to apply softmax classifier to the dataset. What will be the shape of the weights matrix W assuming that the bias trick has been done?

$($b$)$ In plain English and using the data as context, explain what each of the following represents assuming indexing starts from $1$:

$w_{i,2},w_{4,i},w_{1,8},w_{2,5}$

$($c$)$ Suppose the gradient of the loss with respect to some weight parameter evaluated at its current value is $4.$ Justify what will happen to the loss if we increase that weight parameter a little bit while keeping the other parameters fixed? What if we decrease it a little bit?