从 $\mathbf{R}^2$ 的基 $\pmb{\alpha}_1 = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \pmb{\alpha}_2 = \begin{pmatrix} 1 \\ -1 \end{pmatrix}$ 到基 $\pmb{\beta}_1 = \begin{pmatrix} 1 \\ 1 \end{pmatrix}, \pmb{\beta}_2 = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ 的过渡矩阵为