# 向量组的线性相关性与秩（C019）

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## 选项

[A].   $\mathrm{r}\left(\boldsymbol{\beta}_{1}, \boldsymbol{\beta}_{2}, \cdots, \boldsymbol{\beta}_{\mathrm{t}}\right)$ $=$ $\mathrm{r}\left(\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{\mathrm{s}}\right)$

[B].   $\mathrm{r}\left(\boldsymbol{\beta}_{1}, \boldsymbol{\beta}_{2}, \cdots, \boldsymbol{\beta}_{\mathrm{t}}\right)$ $<$ $\mathrm{r}\left(\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{\mathrm{s}}\right)$

[C].   $\mathrm{r}\left(\boldsymbol{\beta}_{1}, \boldsymbol{\beta}_{2}, \cdots, \boldsymbol{\beta}_{\mathrm{t}}\right)$ $\geqslant$ $\mathrm{r}\left(\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{\mathrm{s}}\right)$

[D].   $\mathrm{r}\left(\boldsymbol{\beta}_{1}, \boldsymbol{\beta}_{2}, \cdots, \boldsymbol{\beta}_{\mathrm{t}}\right)$ $\leqslant$ $\mathrm{r}\left(\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{\mathrm{s}}\right)$

$\mathrm{r}\left(\boldsymbol{\beta}_{1}, \boldsymbol{\beta}_{2}, \cdots, \boldsymbol{\beta}_{\mathrm{t}}\right)$ $\leqslant$ $\mathrm{r}\left(\boldsymbol{\alpha}_{1}, \boldsymbol{\alpha}_{2}, \cdots, \boldsymbol{\alpha}_{\mathrm{s}}\right)$