已知向量 $\alpha_1=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right), \alpha_2=\left(\begin{array}{l}2 \\ 1 \\ 1\end{array}\right), \beta_1=\left(\begin{array}{l}2 \\ 5 \\ 9\end{array}\right), \beta_2=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$, 若 $\gamma$既可由 $\alpha_1, \alpha_2$ 线性表示，也可由 $\beta_1, \beta_2$ 线性表示，则 $\gamma=$ ( )
$\text{A.}$ $k\left(\begin{array}{l}3 \\ 3 \\ 4\end{array}\right), k \in \mathbf{R}$
$\text{B.}$ $k\left(\begin{array}{c}3 \\ 5 \\ 10\end{array}\right), k \in \mathbf{R}$
$\text{C.}$ $k\left(\begin{array}{c}-1 \\ 1 \\ 2\end{array}\right), k \in \mathbf{R}$
$\text{D.}$ $k\left(\begin{array}{l}1 \\ 5 \\ 8\end{array}\right), k \in \mathbf{R}$