设向量组 $\boldsymbol{\alpha}_1=\left(\begin{array}{l}1 \\ 2 \\ 1\end{array}\right), \boldsymbol{\alpha}_2=\left(\begin{array}{l}2 \\ k \\ 0\end{array}\right), \alpha_3=\left(\begin{array}{l}4 \\ 1 \\ 2\end{array}\right)$ 线性相关, 求常数 $k$, 并找出一个最大无关组, 并用该最大无关组线性表示其余向量
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