I have some equations which include some parameters and variables. Each variable defines and also exists in other equations. these are my equations:
syms Pof s Pon teta landa PIon PIof PISC
Pof = (s * y - teta T * teta - landa Pi * landa alpha * p Pon * b1 w * b2)/(2 * b2);
s = -(y * (w - Pof))/q;
Pon = (q * s * y 2 * w * y - 2 * w * y^2 2 * q * alpha 2 * q * Pi * landa - q * teta 3 * q * T * teta - q * landa q * Pi * landa - q * alpha * p - 2 * y * Pof 2 * y^2 * Pof C * q * b1 q * w * b2)/(2 * q * b1);
teta = (C - 3 * C * T - Pon 3 * T * Pon)/2 * q;
landa = (-1/2) * (-1 Pi) * (C - Pon);
Don = (1-p) * alpha - b1 * Pon b2 * Pof - (1-y) * s T * teta landa * Pi;
Dof = p * alpha - b1 * Pof b2 * Pon y * s - (1-T) * teta - landa * (1-Pi);
PIon = (Pon-C) * Don - (1/2) * n * teta^2 - (1/2) * q * landa^2;
PIof = (Pof-w) * Dof - (1/2) * L * s^2;
PISC = PIon PIof;
How I can solve these in order to get a numeric answer for each variable? (I don't want parametric answers)
CodePudding user response：
The equations as stated are
which can be arranged as a linear system A x = b as follows
which you solve in Matlab as x = A \ b
On further investigation, it seems A is singular since it's 10×8 in size and cannot be inverted. So a least-squares solution is needed where
x = inv(AT* A)* AT b