从 $\mathbf{R}^{2}$ 的基 $\boldsymbol{\alpha}_{1}=\left(\begin{array}{l}1 \\ 0\end{array}\right), \boldsymbol{\alpha}_{2}=\left(\begin{array}{c}1 \\ -1\end{array}\right)$ 到基 $\boldsymbol{\beta}_{1}=\left(\begin{array}{l}1 \\ 1\end{array}\right), \boldsymbol{\beta}_{2}=\left(\begin{array}{l}1 \\ 2\end{array}\right)$ 的过渡矩阵为