This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 NullSpace NullSpace[ m ] gives a list of vectors that forms a basis for the null space of the matrix m. NullSpace works on both numerical and symbolic matrices. 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. The default setting is ZeroTest -> Automatic. A Method option can also be given. Possible settings are as for LinearSolve. See the Mathematica book: Section 3.7.8. See also: LinearSolve, RowReduce, SingularValues. Further Examples The nullspace of a non-singular matrix is the trivial vector space. In other words, no nonzero vector gets multiplied to the zero vector. In[1]:= Out[1]= This nullspace has dimension . In[2]:= Out[2]= We check the result. In[3]:= Out[3]= This set of vectors spans the nullspace of the x matrix. In[4]:= Out[4]= Multiplying any linear combination of these vectors by the matrix gives the zero vector. In[5]:= Out[5]= We simplify by expanding. In[6]:= Out[6]= The rank of the matrix is the difference between the number of columns and the dimension of the nullspace. In[7]:= Out[7]=