## Null space, basis

Suppose that the homogeneous equation  has nontrivial solutions. Since general solutions are expressed in the parametric vector form, the collection of general solutions

 (11)

is spanned by , and called the null space of . Furthermore, if are linearly independent, then the column vectors  are called a basis of the null space of .

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

Department of Mathematics