Question: In Example 3 we showed that an appropriate choice of basis could greatly simplify the computation of the values of a sequence of the form

In Example 3 we showed that an appropriate choice of basis could greatly simplify the computation of the values of a sequence of the form Av, A2v, A3v, ( ( ( ( Exercises 1 and 2 require an approach similar to that in Example 3
1. Let

And

(a) Show that S is a basis for R2.
(b) Find [v] S.
(c) Determine a scalar (1 such that Av1, = (1v1.
(d) Determine a scalar (2 such that Av2 = (2v2.
(e) Use the basis S and the results of parts (b) through (d) to determine an expression for Anv that is a linear combination of v1 and v2.
(f) As n increases, describe the limiting behavior of the sequence Av, A2v, A3v, ( ( ( ( Anv, ( ( ( (
2. Let

And

Follow the directions for (a) through (f) in Exercise 13.

0.85-0.55 -| 1.10 0.80 v=[2] 2 4 3 3

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