Solving symbolic array.

I am working with symbolic vector of 1xN size. The vector contains N eqations in the from of

X == a + b + c

Y == X*(d + e + f)

Z == Y + X

I am suing subs to substitute the coefficients a b c d e f with numeric values. The result is in the form of

X == g

Y ==X*h

Z == Y +X

It sould be quite straigh forward to solve for Z since all variables are numeric, but for crying out loud I cannot make matlab to solve for Z.

Any ideas?

[Torsten]

Please include your code so far.

[Kristian Dimitrov]

This are the type of inputs that i am using

syms a b c d e
eqn = transpose(str2sym("[X == a+b+c, Y == X*(d+e), Z == X+Y]"));
eqn_S = subs(eqn,{a,b,c,d,e},{[1 2 3 4 5]});

and the outout i am getting

eqn_S =

X == 6

Y == 9*X

Z == X + Y

I tried vpa solve etc. but cannot find syntaxis that works properly to solve for Z.

One way i tried to solve it to solve each row separately and substitute its value in the following equations, but there must be more elegant solution to the problem.

Answer 1

[Kristian Dimitrov]

vpasolve works perfetcly to solve it numerically.

syms a b c d e
eqn = transpose(str2sym("[X == a+b+c, Y == X*(d+e), Z == X+Y]"));
eqn_S = subs(eqn,{a,b,c,d,e},{[1 2 3 4 5]});
vpasolve(eqn_S)

[Torsten]

syms a b c d e X Y Z
eqn = transpose(str2sym("[X == a+b+c, Y == X*(d+e), Z == X+Y]"))

eqn = 

sol = solve(eqn,[X,Y,Z]);

sol = struct with fields:
    X: a + b + c
    Y: (d + e)*(a + b + c)
    Z: a + b + c + a*d + a*e + b*d + b*e + c*d + c*e

sol.Z = simplify(sol.Z)

sol = struct with fields:
    X: a + b + c
    Y: (d + e)*(a + b + c)
    Z: (d + e + 1)*(a + b + c)

subs(sol,[a,b,c,d,e],[1,2,3,4,5])

ans = struct with fields:
    X: 6
    Y: 54
    Z: 60