Suppose you have a neural network with linear activation functions

Suppose you have a neural network with linear activation functions. That is, for each unit the output is some constant
c times the weighted sum of the inputs.
(a) (15 points) Assume that the network has one hidden layer. For a given assignment to the weights w, write down
the equations for the value of the units in the output layer as a function of w and the input layer x, without any explicit
mention of the output of the hidden layer. Show that there is a network with no hidden units that computes the same
function.
(b) (10 points) Repeat the calculation in (a), but this time do it for a network with any number of hidden layers.
(c) (15 points) Suppose a network with one hidden layer and linear activation functions has n input and output nodes
and h hidden nodes. What effect does the transformation in (a) to a network with no hidden layers have on the total
number of weights? In particular, discuss the case h n.