Question 5. Certain dynamical systems can be studied by examining powers of a matrix, such as those below. Use l-'IATLAB, or any other matrix calculator software or website, to determine what happens to A." and B" as 1: increases (for example, try I; = 2, . . . , 16). 4 .2 3 0 .2 .3 A = 3 .6 3 B = .1 .6 .3 3 .2 4 .9 .2 .4 {a} 'What does the limiting behaviour of A" and B".. as k > so, seem to be? 2 pts (1)} Identify what is special about A and B. 2 pts {c} Now make up a few other examples of the same type of matrix: and investigate large powers of those other matrices of this type. You don't need to submit all your working and investigations: only writeup a short summary of what you generally observed. 2 pts {d} Make a conjecture about the behaviour of large powers of matrices of this type. 2 pts