Suppose in a convolutional layer, given an input image matrix $x$ and a filter $W,$ as follows:

$\backslash$table$[[x=,,,,],[1,0,0,1,0],[0,1,1,0,1],[0,1,1,1,0],[1,0,1,0,0],[0,1,0,1,0]]$

$W=$

$-1$

$1$

$1$

$1$

$-1$

$1$

$1$

$1$

$-1$

$($a$)$ Compute the output of this layer by convolutional operation using stride$=1.(5$pts$)$

$($b$)$ Compute the output after applying max$-$pooling layer $($max$-$pooling size is $2$ and stride$=1)$ to the output you obtained from $($a$).(5$pts$)$