Please explain step by step and show all work.

Shrinkage Estimator

Consider a sample of size $n=80$ generated by the model $y={}_0+{}_1{x}_1+{}_2{x}_2+$dots..$+{}_{20}{x}_{20}+$ where $N(0,1^2),$ and the non$-$zero coefficients are ${}_3=3,{}_{19}=2$ while all other coefficients ${}_i=0$ for

$i3,19$

$($a$)$ What is the key difference between Ridge regression and LASSO when applied to this dataset?

$($b$)$ What happens to the estimated coefficients for ${}_3,$and ${}_{19}$ under LASSO and Ridge regression as the penalty parameter $$ increases?

$($c$)$ Why might ElasticNet be preferred over Ridge or LASSO in some cases?