Solving a system of Linear Equations with constraints. Using Symbolic math.

I have the following system of equations with a constraint:

n equations with n unknowns

Here are all known. (Its a known n*n matrix of values).

The following is my try at a solution. How can I correct it to get the 's

p_ij = [0.5, 0.5; 0.2, 0.8];

length_pi_i = size(p_ij);
length_pi_i = length_pi_i(1);

syms pi [1 length(p_ij)]
assume(sum(pi) == 1);


zero_vector = zeros(length(pi), 1);
eqn = (pi' - (pi * p_ij)' == zero_vector);


M = solve(eqn, pi);
disp(M);

Answer 1

[Tanmay Das]

Hi,

I tried reproducing your steps in MATLAB R2021b release and received the following output in the command window:

pi1: 2/7

pi2: 5/7

I tried verifying the answer manually and the answer seems correct to me.

In case you want to learn more about symbolic functions, you may look into 'syms','assume', and 'solve' function documentation.