How to find vectors that belongs to the nullspace of a matrix?

Question

I have a matrix A:

    A = ( 3   2   -1    4
          1   0    2    3 
         -2  -2    3   -1)

After row-transformations I have arrived at:

  A = ( 1   0    2      3  | 0
        0   1  -7/2   -5/2 | 0
        0   0    0      0  | 0 )

Now I have the vector x from A*x:

x1          -2               -3
x2  = x3 * (7/2)  +   x4 * ( 5/2 )
x3           1                0
x4           0                1

Now my N(A) of my NullSpace of A is:

N(A) = span( [-2, 7/2, 1, 0] , [-3, 5/2, 0, 1] )

So my task now is to find two linearly independent vectors which belong to the null-space of the matrix A? How can I do that?

Answer 1

Just take $\left(-2,\frac72,1,0\right)$ and $\left(-3,\frac52,0,1\right)$. They're linearly independent, right?