Solution
= Solution
For an $m\times n$ matrix, its <row space> is the span of its rows, a subspace of $\mathbb R^n$; its <column space> is the span of its columns, a subspace of $\mathbb R^m$. Its <null space> is $\ker A=\{x\in\mathbb R^n:Ax=0\}$. The <rank of a matrix> is the dimension of its column space, equal to the dimension of its row space. The <rank-nullity theorem> gives $\dim\ker A=n-\operatorname{rank}A$.