The main idea behind SVD$-$based Collaborative Filtering is to approximate the sparse user$-$game matrix with a rank$-$

matrix: $\backslash$Sigma $$

$.$

is also referred to as the number of "factors" which are represented by the columns of $$

or the rows of $$

$.$ Complete the function below that takes in a user$\_$game$\_$mat and a user$\_$idx as usual, and performs SVD$-$based Collaborative Filtering with num$\_$factors and random$\_$state. Likewise, it should return a np$.$ndarray $($or a np$.$matrix$)$ of shape $(1,$ user$\_$game$\_$mat.shape$[1])$ that represents the predicted playtime for each game for the user at user$\_$idx.