Given a three$-$layer perceptron with two inputs $(x_1$ and $x_2),$ a hidden layer containing two neurons, and an output neuron, you are provided with the initial synaptic weights as follows: $w_{31}=0\mathrm{.}62,w_{32}=0\mathrm{.}55,w_{41}=0\mathrm{.}42,w_{42}=-0\mathrm{.}17,w_{53}=0\mathrm{.}35,$ and $w_{54}=0\mathrm{.}81.$ The learning rate $()$ is set to $0\mathrm{.}25.$ Given that the first input vector is $0,1$ with a desired output of $0,$ and the second input vector is $1,1$ with a desired output of $1,$

a$.$ calculate the new synaptic weights after completing two iterations of the backpropagation training process. Assume the sigmoid activation function for neurons.