Q$4.$ For a given rating matrix $Rin{R}^{NM},$ we can use matrix factorization to form

$R$~~$P{Q}^T,$ where $n{R}^{NK}$ and $Qin{R}^{MK}.$

For example, we have a user$-$rating matrix R$.$ For these user$-$item without

the rating scores in $R,$ can we just put $"0"$ to facilitate our optimization in

the matrix factorization? Explain and justify your answer.

How to utilize the matrix factorization for recommendations?