设 $\alpha_1, \alpha_2, \alpha_3$ 是三维向量空间 $\mathbb{R}^3$ 的基, 则由基 $\alpha_1, \alpha_2, \alpha_3$ 到 基 $\alpha_1+\alpha_2, \alpha_2+\alpha_3, \alpha_3+\alpha_1$ 的过渡矩阵为
$\text{A.}$ $\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1\end{array}\right]$
$\text{B.}$ $\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right]$
$\text{C.}$ $\left[\begin{array}{lll}1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right]$
$\text{D.}$ $\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$