# NullSpace

NullSpace[m]

gives a list of vectors that forms a basis for the null space of the matrix m.

# Details and Options

• NullSpace works on both numerical and symbolic matrices.
• The following options can be given:
•  Method Automatic method to use Modulus 0 integer modulus to use Tolerance Automatic numerical tolerance to use ZeroTest Automatic function to test whether matrix elements should be considered to be zero
• NullSpace[m,Modulus->n] finds null spaces for integer matrices modulo n.
• NullSpace[m,ZeroTest->test] evaluates test[m[[i,j]]] to determine whether matrix elements are zero.
• Possible settings for the Method option include "CofactorExpansion", "DivisionFreeRowReduction", and "OneStepRowReduction". The default setting of Automatic switches among these methods depending on the matrix given.

# Examples

open allclose all

## Basic Examples(1)

Find the null space of a 3×3 matrix:

 In[4]:=
 In[2]:=
 Out[2]=

The action of m on the vector is the zero vector:

 In[3]:=
 Out[3]=