= Solution
For an $m\times n$ <matrix> $A$ over the <real numbers>, write its rows as $r_1,\ldots,r_m$ and its columns as $c_1,\ldots,c_n$. Then
$$
\boxed{\begin{aligned}
\operatorname{Row}(A)&=\operatorname{span}\{r_1,\ldots,r_m\}\subseteq\mathbb R^n,\\
\operatorname{Col}(A)&=\operatorname{span}\{c_1,\ldots,c_n\}\subseteq\mathbb R^m,\\
\operatorname{Null}(A)&=\{x\in\mathbb R^n:Ax=0\},\\
\operatorname{rank}A&=\dim\operatorname{Row}(A)=\dim\operatorname{Col}(A).
\end{aligned}}
$$
Thus the <row space> and <column space> consist of all <linear combinations> of the corresponding rows and columns; the <null space> is the <kernel of a linear map> represented by $A$. The <matrix rank> counts independent row or column directions, with row rank equal to column rank.
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