I am having issues attempting to derive this new design matrix. The objective function for the previous question was as follows: $\sum_{i}^{n}(Y_{i}-\mu)^2+\lambda\mu^2$
Find a design matrix $X(\lambda)$, and a data vector $Y(\lambda)$ such that: $\hat\mu_{\lambda} = (X(\lambda)^{T}X(\lambda))^{-1}X(\lambda)^{T} Y(\lambda)$
Hint: $Y(\lambda)$ will generally have to be of length $n+1$ or greater; i.e. you need to add an observation to the original Y, as well as an entry to the original X.
I tried viewing this as a regression problem, where we have $Y=X\beta+\epsilon$.
$Y = (\begin{matrix} Y_{n} \\\ ? \\ \end{matrix})$
$X = (\begin{matrix} 1_n \\\ > \end{matrix})$, but I am stuck figuring out how to add the $\lambda$ penalization in.
