MATLAB: Solve system of equations when symbolic vector is referencing its own elements

Question

I have a script that prints out a symbolic vector "a" in terms of its elements a(1),…,a(n):

   a =
   2610.0 - 0.0001*a5 - 1.0e-6*a7 - 0.01*a3
             - 0.02*a4 - 0.0003*a6 - 3027.0
            1176.0 - 0.0007*a7 - 0.03333*a5
                            266.1 - 0.05*a6
                          - 0.07*a7 - 322.0
                                      64.24
                                     -1.701

"a" is a system of equations where the elements of "a" reference other elements of "a", e.g. a(2) references a(4) and a(6):

        a(2) = - 0.02*a4 - 0.0003*a6 - 3027.0

I want to write a(1),a(2),…,a(n) without any symbols appearing on the right-hand side. In other words, I want to substitute numerical values into the elements of "a".

I've tried solve(), vpasolve(), and subs() but I can't format the output to replace the symbols inside each element.

What am I doing wrong?

Thanks,

Michael

Answer 1

Michael, use

 syms a1 a2 a3 a4 a5 a6 a7
 a   = [a1 a2 a3 a4 a5 a6 a7]';
 eq  = [ 2610.0 - 0.0001*a5 - 1.0e-6*a7 - 0.01*a3,
        -0.02*a4 - 0.0003*a6 - 3027.0,
         1176.0 - 0.0007*a7 - 0.03333*a5,
         266.1 - 0.05*a6,
        -0.07*a7 - 322.0,
         64.24,
        -1.701];
 sol = vpasolve(eq==a);