Question: Certain dynamical systems can be studied by examining powers of a matrix, such as those below. Determine what happens to A k and B k

Certain dynamical systems can be studied by examining powers of a matrix, such as those below. Determine what happens to A^kand B^k as k increases (for example, try k = 2,...,16). Try to identify what is special about A and B. Investigate large powers of other matrices of this type, and make a conjecture about such matrices.

A = = .4 .3 3 .2 .3 .6 .3 .2 .4

A = = .4 .3 3 .2 .3 .6 .3 .2 .4 B = = 0 .1 .9 .2 .6 .2 .3 .3 .4

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