Solve system of Linear Equations with Constraints.

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).

How do I find all the (vector of 's)?

Answer 1

[Matt J]

[V,e]=eig(P.','vector');

[~,imin]=min(abs(e-1));

piVector=V(:,imin)/sum(V(:,imin));

[Matt J]

@atharva aalok Though you haven't mentioned it, I'm assuming P is a stochastic matrix. Otherwise, there is no guarantee the equations have a solution.