a$.)$ Create the adjacency matrix $($cities are replaced with actors$)-$ call the matrix A$.$ The matrix A will be a $1616$ matrix. If the actors were in the same movie together, place a $1$ in the matrix entry. Hint: Spreadsheet programs $($e$.$g$.$ Excel$)$ can be useful in setting up the matrix for part a and getting an output that can be used in parts b$,$ c$,$ d$,$ and e$.($Do NOT use a spreadsheet program for computations in parts b$,$ c$,$ d$,$ and e$!)$

b$.)$ Using your matrix A from part a$.),$ how many degrees of separation is Glenn Close from Kevin Bacon? Assume the same movie is $1$ degree of separation, etc. Must show work using your matrix and must use a computer program like Octave or MatLab.

c$.)$ Is the graph in Figure $3$ connected? Must show work using your matrix.

$\begin{array}{cc}\text{K}\text{e}\text{v}\text{i}\text{n}\text{B}\text{a}\text{c}\text{o}\text{n}& \text{G}\text{l}\text{e}\text{n}\text{n}\text{C}\text{l}\text{o}\text{s}\text{e}\\ \text{B}\text{i}\text{l}\text{l}\text{P}\text{a}\text{x}\text{t}\text{o}\text{n}& \text{N}\text{i}\text{c}\text{o}\text{l}\text{e}\text{K}\text{i}\text{d}\text{m}\text{a}\text{n}\\ \text{T}\text{o}\text{m}\text{H}\text{a}\text{n}\text{k}\text{s}& \text{J}\text{o}\text{h}\text{n}\text{G}\text{i}\text{e}\text{l}\text{g}\text{u}\text{d}\\ \text{D}\text{o}\text{n}\text{a}\text{l}\text{d}\text{S}\text{u}\text{t}\text{h}\text{e}\text{r}\text{l}\text{a}\text{n}\text{d}& \text{V}\text{e}\text{r}\text{n}\text{o}\text{n}\text{D}\text{o}\text{b}\text{t}\text{c}\text{h}\text{e}\text{f}\text{f}\\ \text{J}\text{o}\text{h}\text{n}\text{B}\text{e}\text{l}\text{u}\text{s}\text{h}\text{i}& \text{P}\text{a}\text{u}\text{l}\text{H}\text{e}\text{r}\text{b}\text{e}\text{r}\text{t}\\ \text{M}\text{e}\text{r}\text{y}\text{l}\text{S}\text{t}\text{r}\text{e}\text{e}\text{p}& \text{L}\text{l}\text{o}\text{y}\text{d}\text{B}\text{r}\text{i}\text{d}\text{g}\text{e}\text{s}\\ \text{K}\text{a}\text{t}\text{e}\text{W}\text{i}\text{n}\text{s}\text{l}\text{e}\text{t}& \text{P}\text{a}\text{t}\text{r}\text{i}\text{c}\text{k}\text{A}\text{l}\text{l}\text{e}\text{n}\\ \text{G}\text{r}\text{a}\text{c}\text{e}\text{K}\text{e}\text{l}\text{l}\text{y}& \text{K}\text{a}\text{t}\text{h}\text{l}\text{e}\text{e}\text{n}\text{Q}\text{u}\text{i}\text{n}\text{l}\text{a}\text{n}\end{array}$