TITLE: unit length vector in kernel of matrix
QUESTION [5 upvotes]: congratulation  you all   passed  festival(new year,christmas),guys i have question related kernel of matrix,namely suppose we have  following matrix
$$
A=
  \begin{bmatrix}
      1 & -1 & 0 \\
      0 & 0 & 1  \\
    0 & 0 & 0  \\
    \\
  \end{bmatrix}
$$
we should find  unit-length  vector of kernel of matrix,for kernel  i think  we should find such null space  or  vector  $x$  for which
$A*x=0$
as it is indicated  on following  wikepedia  site
[http://en.wikipedia.org/wiki/Kernel_(matrix)][1]

but i think it has  many solution because  if we interpret  $x$  as  $x=[x_1,  x_2,  x_3]$ we get
$x_1-x_2+0*x_3=0$
$x_3=0$
so we have
$x_1=x_2$
$x_3=0$
how can i continue?please help me

REPLY [3 votes]: Yes, for a vector in the kernel, $x_2$ is arbitrary, $x_1 = x_2$, and $x_3 = 0$, i.e. the vector is $\displaystyle\pmatrix{x_2\cr x_2\cr 0\cr}$.  Now use the condition that the length should be $1$.