1. Test the associate law of multiplication with the following matrices: A = [ 5 3 0 5 ] B = [ 8 0 7 1 3 2 ] C = [ 1 0 0 3 7 1 ] Given A = [ 1 5 7 0 2 4 ] , b = [ 9 6 0 ] , and x = [ 1 2 ]

2. Calculate: (a) Ab (b) AIb (c) (d)

Does the insertion of I in (b) affect the result in (a)? Does the deletion of I in (d) affect the result in (c)?

3. Consider the situation of a mass layoff (i.e., a factory shuts down) where 1,200 people become unemployed and now begin a job search. In this case there are two states: employed (E) and unemployed (U) with an initial vector

0 = [ ] = [0 1, 200]

Suppose that in any given period an unemployed person will find a job with probability .7 and will therefore remain unemployed with a probability of .3. Additionally, persons who find themselves employed in any given period may lose their job with a probability of .1 (and will have a .9 probability of remaining employed)

a. Set up the Markov transition matrix for this problem.

b. What will be the number of unemployed people after (i) 2 periods; (ii) 3 periods; (iii) 5 periods; (iv) 10 periods?

c. What is the steady-state level of unemployment?