MCh =[ 1 0 -1 0
5 0 0 -1
0 2 -3 -1
0 1 -4 0];
rank(MCh)
You wish to solve the 4x4 homogeneous linear system. It will have a valid non-zero solution only if the rank is less than full rank. Since the rank is 3, it has a solution. The way to solve it is to find the nullspace of the matrix. That is:
format long
X = null(MCh)
MCh*X
As you can see, this solves the problem (if we ignore the floating point trash that remains.) The vector that results is normalized to have unit norm.
If you want an exact solution, this will do it:
Xsym = null(sym(MCh))
And there we see a nice simple form falls out.
