已知向量 $\alpha=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], \beta=\left[\begin{array}{l}1 \\ 0 \\ k\end{array}\right]$, 若矩阵 $\alpha \beta^{\mathrm{T}}$ 相似于矩阵 $\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$, 则 $k=$
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