It looks like you want to find all of the vectors satisfying Ax = 0 for some singular matrix , A. If so, you can do this using
This returns a basis for the null space of a matrix A.
In your case MATLAB returns X = [0.5;0.5;0.5;0.5], any multiple of this will satisfy your equation,
so for example 2*[0.5;0.5;0.5,0.5] = [1;1;1;1] is a solution and you can verify that A*[1;1;1;1]=0
To find out more about the null function type doc null on the command line in MATLAB