In the assignment, we consider a dynamic system illustrated by the box diagram 0.5 81 0.2 0.1 0.3 0.2 p3 0.4 0.5 0.2 $2 0.6 Exercise 1. Find the transition matrix M for the system, and explain what we mean by a stochastic matrix. Show that M is stochastic. Exercise 2. Calculate the characteristic polynomial of M. Since M is stochastic, we know that the largest eigenvalue of M is 1. Use that to calculate the other eigenvalues. Exercise 3. Also calculate the eigenvectors of M. Do the eigenvectors form a basis for R^3?Give a brief justification for your answer. The eigenvectors form a basis for R^3 if any vector in R3 can be written as a linear combination of eigenvectors. Mail 23:15 I need help with these tasks. Exercise 1. We start from a vector v0 = Write this vector as a linear combination of eigenvectors. ? 3 "-(-) 2 Exercise 2. Find an expression for Mnvo for an arbitrary positive integer n. What happens when V1= n? Exercise 3. Let w = R be given as a linear combination of the vectors (). og V2 || (-9) ( What happens to w when we multiply it by M times? coursehero.com Q&A