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

$x=$

$1,0,0,1,0$

$0,1,1,0,1$

$0,1,1,1,0$

$1,0,1,0,0$

$0,1,0,1,0$

$W=$

$-1,1$

$1,-1,1$

$1,1,-1$

$($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$)$