syms s X Y Z
l1 = X*s - 1 == 3*X + Y + Z + 2/s
l2 =Y*s == - X - Y - 1/s^2
l3 =Z*s - 2 == X - Z - (s - 1)/s^2
[Xsol,Ysol,Zsol]=solve([l1,l2,l3],[X,Y,Z])
Up to this point, you have done nothing wrong. Xsol, Ysol, and Zsol are all validly defined expressions of x, y, and z.
Then you tried to use partfrac, as applied to a vector, composed of [xsol,ysol,zsol].
help partfrac
You could have applied partfrac to any one of them.
Xsolpf = partfrac(Xsol)
However, partfrac is not vectorized. And when you tried that as you did, it gave you an error. The point is, you could just have called partfrac three times. But not everything you write in MATLAB will be vectorized to work as you might hope it should work. Code is only code. As much as we wish it would do so, it cannot do more than it was written to do.
Could you have done like this?
XYZsol = partfrac([Xsol,Ysol,Zsol])
And then separated each of the three components into a separate result? Well, yes.
XYZsol(1)
XYZsol(2)
XYZsol(3)
