Solution
= Solution
Over the underlying <field> $F$, the <row space> is the <linear span> of the row <vectors> of $A$, a <vector subspace> of $F^n$. The <column space> is the <linear span> of its column <vectors>, a <vector subspace> of $F^m$. The <null space> is
$$
\ker A=\{x\in F^n:Ax=0\},
$$
a <vector subspace> of the domain. The <column space> is the <image of a linear map> represented by $A$; the <null space> is its <kernel>.