Solutions $($your work starts here$)$

$(0\mathrm{.}5$ points$)$ The following is the initial adjacency matrix for the Floyd algorithm. Proof that $D^{(1)}[5][2]=4$ using a Dynamic Programming approach. Show all your work to support your proof.

$\backslash$table$[[,1,2,3,4,5],[1,0,2,3,8,2],[2,6,0,7,9,7],[3,9,4,0,1,12],[4,3,2,4,0,2],[5,2,7,3,1,0]]$