\begin{aligned} &\text { 1. (5 points) If } a, b \in \mathbb{R}, \text { find the LU factorization of } A=\left(\begin{array}{ccc} 2 & 1 & 8 \\ 2 a &

a+3 & 8 a+9 \\ -6 & 3 b-3 & 9 b-20 \end{array}\right) \text { with } 1 \mathrm{~s}\\ &\text { on the diagonal of L. } \end{aligned}