Finding the Position Vector and Metric Tensor

syms ax ay a vx vy vz x0 y0 z0
a=[ax ay az]
v=[vx vy vz]
r=[x0 y0 z0]
x=sym(zeros(4))
dx=sym(zeros(4))
g_ab=sym(zeros(4,4))
gupab=sym(zeros(4,4))
x=[t a(1)/2*t^2+v(1)*t+r(1) a(2)/2*t^2+v(2)*t+r(2) a(3)/2*t^2+v(3)*t+r(3)]
dx=diff(x,t)
for b=1:4
    for a=1:4
        g_ab(a,b)=-(dx(a))^-1*(dx(b))^-1
    end
end
gupab = inv(g_ab)

Error code:

??? Error using ==> sym.inv
Error, (in inverse) singular matrix

Error in ==> PositionVector at 21
gupab = inv(g_ab)