Problem $2$

$($Practice of vector$$based backpropagation$).$

You are required to calculate the gradients of f$($x$,$ W$)=$ Wx$,$ with respect to W and x$.$

Set w $=[$

$212$

$131$

$747$

$]$ and x $=[$

$1$

$0$

$1$

$]$

$($a$)$ Use computational graph for calculation

$($b$)$ Based on$($a$),$ write a program to implement the computational graph and verify your answer in $($a$).$

You can use vectorized approach to simply your codes.