Column stochastic matrix/2/Eigenvector and eigendistribution/Exercise

Find an eigenvector for the matrix

${\begin{pmatrix}p_{1}&p_{2}\\1-p_{1}&1-p_{2}\end{pmatrix}}$

with

${}0\leq p_{1},p_{2}\leq 1\,$

to the eigenvalue ${}p_{1}-p_{2}$. Is it an eigendistribution?

Create a solution