Problem #$2$: Apply the F matrix algorithm in the second handout $($available under Cancas as ShortestPath$\_$F$\_$Matrix$\_$algorithm.pdf$)$ to the directed graph above. Calculate and show the following matrices with rows and columns corresponding to the vertices $v1,v2,v3,v4,v5,v6$ in order. $(7$ points, one point for each.$)$

$($i$)F^{(0)},$

$($ii$)F^{(1)},$

$($iii$)F^{(2)},$

$($iv$)F^{(3)},$

$($v$)F^{(4)},$

$($vi$)F^{(5)},$

$($vii$)F^{(6)}.$