Hello there MHF,

I am working on a massive systems of equations problem (7 equations, 50+ variables) with which I could really use your help! I would rather not muddy the water with substantive context, but for those of you who are interested, the problem essentially arises when you have, in this case, 7 observed populations (groups) with observed sample sizes, but you know there is bidirectional misclassification going on between all populations. You know the observed group sizes and all rates of misclassification and are ultimately trying to solve for the true sample sizes.

I have found some online systems of equations calculators that will give me solutions for the 2 and 3 group problems (2 and 3 equations), but it breaks down when there are 4 or more equations (I was using https://quickmath.com/webMathematica...e/advanced.jsp). Is there a better website for 7 equations?

Anyway, here are all 7 equations with all variables. I am trying to solve for T_1, T_2, T_3, T_4, T_5, T_6, T_7.

- N_1 = T_1 – (T_1*a + T_1*c + T_1*g + T_1*m + T_1*u + T_1*E) + (T_2*b + T_3*d + T_4*h + T_5*n + T_6*v + T_7*F)
- N_2 = T_2 – (T_2*b + T_2*e + T_2*i + T_2*o + T_2*w + T_2*G) + (T_1*a + T_3*f + T_4*j + T_5*p + T_6*x + T_7*H)
- N_3 = T_3 – (T_3*d + T_3*f + T_3*k + T_3*q + T_3*y + T_3*I) + (T_1*c + T_2*e + T_4*l + T_5*r + T_6*z + T_7*J)
- N_4 = T_4 – (T_4*h + T_4*j + T_4*l + T_4*s + T_4*A + T_4*K) + (T_1*g + T_2*i + T_3*k + T_5*t + T_6*B + T_7*L)
- N_5 = T_5 – (T_5*n + T_5*p + T_5*r + T_5*t + T_5*C + T_5*M) + (T_1*m + T_2*o + T_3*q + T_4*s + T_6*D + T_7*N)
- N_6 = T_6 – (T_6*v + T_6*x + T_6*z + T_6*B + T_6*D + T_6*O) + (T_1*u + T_2*w + T_3*y + T_4*A + T_5*C + T_7*P)
- N_7 = T_7 – (T_7*F + T_7*H + T_7*J + T_7*L + T_7*N + T_7*P) + (T_1*E + T_2*G + T_3*I + T_4*K + T_5*M + T_6*O)

Many thanks!

Jnonymous