设 $A, P$ 均为 3 阶方阵, $P^T$ 为 $P$ 的转置矩阵, 且 $P^T A P=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right]$, 若 $P=$ $\left(\alpha_1, \alpha_2, \alpha_3\right), Q\left(\alpha_1+\alpha_2, \alpha_2, \alpha_3\right)$, 则 $Q^T A Q$ 为
A. $\left[\begin{array}{lll}1 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$
B. $\left[\begin{array}{lll}2 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 2\end{array}\right]$
C. $\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2\end{array}\right]$
D. $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$