Editing Linear subspace (section)

===Column space and row space===
{{main|Row and column spaces}}
A system of linear parametric equations in a finite-dimensional space can also be written as a single matrix equation:

:<math>\mathbf{x} = A\mathbf{t}\;\;\;\;\text{where}\;\;\;\;A = \left[ \begin{alignat}{2} 2 && 3 & \\ 5 && \;\;-4 & \\ -1 && 2 & \end{alignat} \,\right]\text{.}</math>

In this case, the subspace consists of all possible values of the vector '''x'''. In linear algebra, this subspace is known as the column space (or [[image (mathematics)|image]]) of the matrix ''A''. It is precisely the subspace of ''K''<sup>''n''</sup> spanned by the column vectors of ''A''.

The row space of a matrix is the subspace spanned by its row vectors. The row space is interesting because it is the [[orthogonal complement]] of the null space (see below).