Problem $2.[15$ points$]$ Suppose we run a ridge regression with regularization parameter $\backslash$lambda on a training$$data with a single variable S $=\{($x$1,$ y$1),($x$2,$ y$2),...,($xn$,$ yn$)\},$ and get coefficient w$1$ in R $($for simplicity,$$we assumed the data are centered and no bias $($intercept$)$ term is needed$).$ We now include an exact copy$$of first feature to get a new training data as$$S$=\{([$x$1,$ x$1],$ y$1),([$x$2,$ x$2],$ y$2),...,([$xn$,$ xn$],$ yn$)\}$where each training example is a $2$ dimension