Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2017 / Paper 2 / 17 / c / Solution

At a steady state, $K{\mathbf{y}}_0={\mathbf{f}}_0$. All eigenvalues of $K$ are nonzero, so it is invertible andFor the specified constant source this givesIndeed the first two rows of $K{\mathbf{y}}_0$ each give one, and the third gives $4(1/4)=1$.