Computing the closed form solution in part $(2)$ could be computational burden for large

number of users or movies. A remedy for this would be using iterative optimization algorithms

such as Stochastic Gradient Descent $($SGD$)$ where you sample movies in updating the latent

features for users and sample users in updating the latent features of movies. Derive the

updating rules for u

$($t$)$

i and v $($t$)$

j at tth iteration of SGD$.$ Show the detailed steps