Why in the Ridge regression, the coefficients cannot be 0? In the second answer (https://stats.stackexchange.com/a/368426/287815) to the question (Why will ridge regression not shrink some coefficients to zero like lasso?), the OP found out that,
$β = /(^2+λ)$
My question:
Can't the $\beta$ be 0 if one of x or y is a zero vector?

What the referred answers say is that in ridge regression the regularization does not shrink the parameters to exact zeros. It doesn't say that the parameters cannot be zeros, just that it's not what the regularization does. Your example with zero vectors is a pathological case and even without regularization, the parameter would be zero, so it has nothing to do with regularization.
