Linear system/Kernel/Relation/Remark

For an ${\displaystyle {}m\times n}$-matrix ${\displaystyle {}M}$, the kernel of the linear mapping

${\displaystyle K^{n}\longrightarrow K^{m},x\longmapsto Mx,}$

given by ${\displaystyle {}M}$ is just the solution space of the homogeneous linear system

${\displaystyle {}Mx=0\,.}$