Suppose that the homogeneous equation has nontrivial solutions. Since general solutions are expressed in the parametric vector form, the collection of general solutions
In Matlab/Octave the function null(A) returns a matrix containing column vector 's which are a basis of the null space of . The choice of vectors is not necessarily unique. Matlab/Octave produces the vectors 's of unit norm (i.e., ; see Section 6.1).
EXAMPLE 3. Find a basis for the null space of the matrix