Consider a $2$D input matrix X:

X $=$

$$

$$

$120130$

$013212$

$210011$

$102320$

$011201$

$203112$

$$

$$

You are given a $2$D filter $($kernel$)$ W:

W $=$

$$

$11$

$02$

$$

$($a$)$ Perform a valid convolution of the input X with the filter W $($stride $=1,$ no padding$).$

Show all steps and provide the resulting matrix.