Singular Values & the SVD · Challenge problem

Ridge (Tikhonov) regression replaces the least-squares solution by $x_\lambda = (A^{T}A + \lambda I)^{-1}A^{T}b$. For $A = \begin{pmatrix}2 & 1\\1 & 2\end{pmatrix}$, $b = \begin{pmatrix}3\\1\end{pmatrix}$ and $\lambda = 1$, find the sum of the two components of $x_\lambda$.