Problem $3$: Vector Representation of Neural Networks $(20$ points$)$

Neural networks can be efficiently represented and computed using vectors and matrices. In this

exercise, you will revisit the $2-$layer MLP in Problem $1.$ Assuming the input feature $(x_1,x_2)=(2,-3)$

and using the provided values of weights and biases, please do the following.

Write down the Weight matrix, $W^{[1]},$ and the bias vector, $b^{[1]},$ for the hidden layer.

Write down the Weight matrix, $W^{[2]},$ and the bias vector, $b^{[2]},$ for the output layer.

Calculate $Z^{[1]},A^{[1]},Z^{[2]}$ and $A^{[2]}$ using the following equations.

$Z^{[1]}=W^{[1]}x+b^{[1]},A^{[1]}=f^{[1]}(Z^{[1]})$

$Z^{[2]}=W^{[2]}{A}^{[1]}+b^{[2]},A^{[2]}=f^{[2]}(Z^{[2]})$

where the activation function $f^{[1]}(z)=$sigmoid and $f^{[2]}(z)=$ReLU.