Consider the matrices P =

Question

3 1
1 3

and S =
4 2
2 4

Calculate P^n and S^n for different values of n and describe any patterns you observe.

I cannot find any patterns at all. I would really appreciate any help at all. Thanks!

Answer 1

I also have to generalize any patterns in the following matrix:

k+1 k-1
k-1 k+1

by considering various values of k.

Answer 2

describe the patterns used in the tables in activties 2 and 3

Answer 3

describe the patterns in the table in activties 2 and 3

Answer 4

1x3=3
3x4=12

2x3=6
6x4=24