Questions on matlab.

1. Suppose,

A=[0.999375 0.000625; 0.000125 0.999875]

and

x0= [10 0]

a. Find the eigenvalues of A and determine whether A will converge to a steady state.

Output your answer to the command window.

b. What is the location of the system after 10 units of time?

c. What is the location of the system after 100 units of time?

d. What is the location of the system after 1000 units of time?

e. What is the location of the system after 10000 units of time?

f. What is the location of the system after 100000 units of time?

g. What is the location of the system after 1000000 units of time?

h. Plot the entire trajectory followed by the system during 1000000 units of time with a

proper title and axis labels. (Hint: Create a 1 by 2 subplot with values for the first

coordinate plotted on the first subplot and values for the second coordinate plotted on

the second subplot. Here, your x-axis will be the time iteration and your y-axis will

be the value of the plotted coordinate.) You will need to generate the data points for

each iteration. Write your code in the most efficient way.