Prove that if A is a stochastic matrix and p is a probability vector. then Ap i> a probability vectot.

M344 Section 7.4 Notes- Basic Theory of Systems of First Order Linear Equations 1-31-17 ′ 1= 11( 1+ 12( 2+ ⋯+ 1( + 1) Consider system { ⋮ ; closely parallels single linear = ( + ( + ⋯+ ( + () ℎ 1 2 2 differential equation of order o Follows same general lines as material in 3.2 (solving linear homogeneous ODEs) and 4.1 (general theory of ℎ order ODEs) o Most efficient to write s