$1.($Exercise $9\mathrm{.}3\mathrm{.}1)$ Consider a utility matrix below, representing the ratings, on a $1-5$ star scale, of eight items, a through h$,$ by three users A$,$ B$,$ and C$.$ Compute the following fro the data of this matrix.

a$)$ Treating the utility matrix as boolean $($with rating as $1$ and without rating as $0),$ compute the Jaccard distance between each pair of users;

b$)$ Repeat a$)$ but use the cosine distance.

c$)$ Treat ratings of $3,4,$ ad $5$ as $1,$ and $1,2$ and blank as $0.$ Compute the Jaccard distance between each pair of users.

d$)$ Repeat c$),$ but use the cosine distance.

e$)$ Normalize the utility matrix by subtracting from each nonblank entry the average value for its user.

f$)$ Using the normalized matrix from e$),$ compute the cosine distance between each pair of users.