Editing Linear subspace (section)

===Basis for a null space===
:'''Input''' An ''m''&nbsp;×&nbsp;''n'' matrix ''A''.
:'''Output''' A basis for the null space of ''A''
:# Use elementary row operations to put ''A'' in reduced row echelon form.
:# Using the reduced row echelon form, determine which of the variables {{nowrap| ''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x<sub>n</sub>''}} are free. Write equations for the dependent variables in terms of the free variables.
:# For each free variable ''x<sub>i</sub>'', choose a vector in the null space for which {{nowrap|1= ''x<sub>i</sub>'' = 1}} and the remaining free variables are zero. The resulting collection of vectors is a basis for the null space of ''A''.
See the article on null space for an [[Kernel (matrix)#Basis|example]].