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

is spanned by , and called the

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