Suppose you had 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. 

1. Assume that the network has one hidden layer. For a given assignment to the weights w, write down 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.
2. Repeat the calculation in part (a), but this time do it for a network with any number of hidden layers.
3. 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 part (a) to a network with no hidden layers have on the total number of weights? Discuss the case h << n.