Q$\mathrm{.}1)[$Total Marks:$10]L^2$ regularization function is given by the following:

tilde$(J)(w$;$x,y)=\frac{}{2}{w}^{T}w+J(w$;$x,y)$

where $$ is the regularization parameter. Derive the optimal solution for the regularized function, i$.$e$.,$

widetilde$(w)$ in terms of the optimal solution of the unregularized function, i$.$e$.,w^{*}.$ The expression should be

able to explain the rotation and the scaling.