问题
已知，$n$ 个 $n$ 维向量 $\textcolor{orange}{\boldsymbol{\alpha}_{1}}$, $\textcolor{orange}{\boldsymbol{\alpha}_{2}}$, $\textcolor{orange}{\cdots}$, $\textcolor{orange}{\boldsymbol{\alpha}_{n}}$ 线 性 相 关 ，则行列式 $\textcolor{cyan}{\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|}$ 具有什么特点？选项
[A]. $\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|$ $>$ $1$[B]. $\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|$ $>$ $0$
[C]. $\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|$ $\neq$ $0$
[D]. $\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|$ $=$ $0$
$\textcolor{cyan}{\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|}$ $\textcolor{red}{=}$ $0$