Include input and output.Include full$-$sentence response.

Consider the following linking matrix showing connections between the websites A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ G$,$ and H:

Enter this matrix into MATLAB with the command

$>>$ L $=[0,0,0,0,1,0,0,0$;

$0,0,0,0,0,0,0,1$;

$0,1/2,0,0,0,0,1,0$;

$1/2,0,1/2,0,0,0,0,0$;

$0,0,1/2,0,0,1,0,0$;

$1/2,0,0,0,0,0,0,0$;

$0,1/2,0,0,0,0,0,0$;

$0,0,0,1,0,0,0,0$;$]$

Let e$0=(1,1,1,1,1,1,1,1)$T$,$ and define en$+1=$ Len $($which is the same as saying en $=$ Lne$0).$ Use MATLAB to compute e$10.$ How large must n be so that each entry of en changes by less than $1\%$ when we increase n by $1?[$Don$\text{'}$t try to get an exact value, just try to get a value for n that's big enough.$]$

In the graph of the network of webpages represented by L$,$ which vertices have an edge going out and pointing toward website C$?$ Which vertices do the edges coming out of C point to$?($Here$,$ by graph we mean a collection of vertices and edges.$)$