The question is about the content$-$based recommendation system. Assume that the database consists of $6$ products with the following $5$ genres:

Product $1$: $\{1,1,0,0,1\}$

Product $2$: $\{1,0,1,1,0\}$

Product $3$: $\{0,1,1,1,1\}$

Product $4$: $\{0,1,1,0,1\}$

Product $5$: $\{1\mathrm{.}1\mathrm{.}1\mathrm{.}0,1\}$

Product $6$: $\{1,0,0,0,1\}$

The user already rated first three products $Pr1,2,$ and $3$ as: $8,4,2$ respectively out $10.$ Show the entire calculation including:

weighted genre matrix

user profile

finding the recommendation and the order of $3$ remaining products.