Implement a function firstdiff$\_$ij in the next cell that takes as its input the variables $i,j$ and $n,$ and returns as its output fij such that fij$=A[i,j]$ according to the rules above.

Reminder: We are not producing a matrix with firstdiff$\_$ij$,$ just one element that may be $0,1,$ or $-1.$ In the setup below, return fij is at the end, so defining the scalar fij is the desired result.

Hint: The command if $)==(10)==(5$ checks if i equals $10$ and $j$ equals $5.$

$"1"\text{'}"$

fij$=$ firstdiff$\_$ij$($i$,j,n$

Inputs:

$\text{'}$i$\text{'},$ row index

$\text{'}$j$\text{'},$ column index

$\text{'}n\text{'},$ length of each side of desired first difference matrix

Output: $\text{'}$ fij $\text{'}$ is the $(\text{'}i\text{'},\text{'}j\text{'})-$th element of the $\text{'}n\text{'}-$dimensional

first difference matrix.

$"\text{'}."\text{'}$

function firstdiff$\_$ij$($i::Integer, j::Integer, n::Integer$)$

if $??$

$??$

elseif $??$

$??$

elseif $(??)$ && $(??)$

$??$

else

$??$

end

return $fi{j}_j$

end