设 $T$ 是线性空间 $R^3$ 上的线性变换，基

$$
\alpha_1=\left(\begin{array}{c}
-1 \\
0 \\
-2
\end{array}\right), \alpha_2=\left(\begin{array}{l}
0 \\
1 \\
2
\end{array}\right), \alpha_3=\left(\begin{array}{l}
1 \\
2 \\
5
\end{array}\right)
$$

在 $T$ 下的像分别为

$$
T\left(\alpha_1\right)=\left(\begin{array}{c}
2 \\
0 \\
-1
\end{array}\right), T\left(\alpha_2\right)=\left(\begin{array}{l}
0 \\
0 \\
1
\end{array}\right), T\left(\alpha_3\right)=\left(\begin{array}{l}
0 \\
1 \\
2
\end{array}\right)
$$

求 $T$ 在基 $\beta_1=\left(\begin{array}{c}-1 \\ 1 \\ 0\end{array}\right), \beta_2=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right), \beta_3=\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)$ 下的矩阵．