Editing Linear subspace (section)

===Null space of a matrix===
{{main|Null space}}
In a finite-dimensional space, a homogeneous system of linear equations can be written as a single matrix equation:

:<math>A\mathbf{x} = \mathbf{0}.</math>

The set of solutions to this equation is known as the [[Null Space|null space]] of the matrix. For example, the subspace described above is the null space of the matrix

:<math>A = \begin{bmatrix} 1 & 3 & 2 \\ 2 & -4 & 5 \end{bmatrix} .</math>

Every subspace of ''K''<sup>''n''</sup> can be described as the null space of some matrix (see {{slink||Algorithms}} below for more).