The following is a DMLP with three hidden layers.

$($Hint$)$ Use Matlab or Python for calculations.

$(1)$ Write the weight matrix $U^1,U^2,U^3,U^4$ as Eq$.(4\mathrm{.}1).$

$(2)$ Find the output $o$ when is input $x=(1,0{)}^T.$ Use the logistic sigmoid as the activation function.

$(3)$ Find the output $o$ when is input $x=(1,0{)}^T.$ Use as the ReLU as the activation function.

$(4)$ If the expected output $o=(1,0{)}^T$ of is $x=(1,0{)}^T,$ explain how reducing the $u_{12}^3$ weight, which is currently $1\mathrm{.}0,$

to $0\mathrm{.}9$ affects the error.