$n$ 个线性无关的 $n$ 维向量的性质(C017)

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 ,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].   $\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|$ $>$ $0$

[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].   $\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|$ $>$ $1$


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$\textcolor{cyan}{\left|\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{n}\right|}$ $\textcolor{red}{\neq}$ $0$