# regularized LLS, trying to compute by hand the optimal weights yields wrong results

given the following dataset $$S = \{(0,1),(1,1),(1,2)\}$$ and the regularized problem $$\sum_{i=1}^3 (y_i - w_1 x_i - w_0)^2 + \lambda w_1^2 \quad \lambda = 1$$ i was tasked with finding the optimal $$w_0 ,w_1$$ that solve this problem and was advised to use the closed form formula, which i dug from my notes: $$\mathbf{\Theta}^* = \operatorname{argmin}_\theta \frac{1}{N} \|X\Theta -y\|_2^2 + \lambda \Theta^TW\Theta \implies \Theta =(X^TX+N\lambda W)^{-1} X^T y$$ I've managed to compute it but the results don't seem to match the correct ones in the text, or the ones my friends got using partial derivatives. I got $$w_0^* = 17/5$$ and $$w_1^* =1/5$$. attached is my calculation, here are the matrices I've defined: $$X = \left[ \begin{array}{cc} 1 & 0 \\1& 1 \\ 1 & 2 \end{array}\right] \quad A = \left[ \begin{array}{cc} 0 & 0 \\0& 1 \end{array}\right] \quad y = \left[ \begin{array}{c} 1 \\1\\ 2 \end{array}\right]$$(A is my stand in for W the weights matrix due to the notation overlap in this particular problem, my W is the formula's Theta - the weights vector).
my attempt: https://i.sstatic.net/fviQh.jpg