Given a two$-$layer neural network and associated weights as shown below:

Assuming that the two hidden layer processing neurons $($i$.$e$.,$ neurons $3$ and $4)$ use a ReLU activation function, and the output layer processing neuron $($i$.$e$.,$ neuron $5)$ uses a logistic $($sigmoid$)$ action function:

$($a$)$ Calculate the output of neuron $5$ for the input vector: neuron $1=2$ and neuron $2=3$

$($b$)$ If the ground truth label of the above input vector is $1,$ measure the cross entropy loss of neuron $5$ and update all weights in the network by using backpropagation optimization and learning rate $=0\mathrm{.}1.$ Hint: please check the weight update formula in the last few slides of lecture $3.$

$($c$)$ Calculate the output of neuron $5$ for the same input vector using the new weights.