问题
根据矩阵秩的性质，$\textcolor{orange}{\mathrm{r}(\boldsymbol{A}+\boldsymbol{B})}$ 与 $\textcolor{orange}{\mathrm{r}(\boldsymbol{A})}$ $\textcolor{orange}{+}$ $\textcolor{orange}{\mathrm{r}(\boldsymbol{B})}$ 之间存在 怎 样 的 关 系 ？选项
[A]. $\mathrm{r}(\boldsymbol{A}+\boldsymbol{B})$ $<$ $\mathrm{r}(\boldsymbol{A})$ $+$ $\mathrm{r}(\boldsymbol{B})$[B]. $\mathrm{r}(\boldsymbol{A}+\boldsymbol{B})$ $=$ $\mathrm{r}(\boldsymbol{A})$ $+$ $\mathrm{r}(\boldsymbol{B})$
[C]. $\mathrm{r}(\boldsymbol{A}+\boldsymbol{B})$ $\geqslant$ $\mathrm{r}(\boldsymbol{A})$ $+$ $\mathrm{r}(\boldsymbol{B})$
[D]. $\mathrm{r}(\boldsymbol{A}+\boldsymbol{B})$ $\leqslant$ $\mathrm{r}(\boldsymbol{A})$ $+$ $\mathrm{r}(\boldsymbol{B})$
$\mathrm{r} \textcolor{yellow}{(}\boldsymbol{\textcolor{orange}{A}}+\boldsymbol{\textcolor{cyan}{B}}\textcolor{yellow}{)}$ $\textcolor{red}{\leqslant}$ $\mathrm{r}\textcolor{yellow}{(}\boldsymbol{\textcolor{orange}{A}}\textcolor{yellow}{)}$ $+$ $\mathrm{r}\textcolor{yellow}{(}\boldsymbol{\textcolor{cyan}{B}}\textcolor{yellow}{)}$