Suppose that 3% of the people who are employed in a certain community's workforce will lose their job each year, and that, of people who are unemployed, 50% find a job in one year. set up a stochastic matrix to represent the changes in the proportions of the workforce that are employed and unemployed from year to year. find a steady-state vector, and interpret the resu 3. let a be defined as below 1 2 2 a 08 2 (a) (2 pts and equation for a. solve this equation to find b) (3 pts) for each of these eigenvalues, find a corresponding eigenvector write out the characteristic polynomial the eigenvalues of a. (c) (3 pts) explain how you know that a is diagonalizable. find matrices p and d such that a = pdp-1, where d is diagonal.