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Find the limiting values of yk and k (k ) if yk+1 = .8yk +.3zk y0 = 0 zk+1 = .2yk +.7zk

Chapter 5, Problem 5.3.10

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QUESTION:

Find the limiting values of yk and k (k ) if yk+1 = .8yk +.3zk y0 = 0 zk+1 = .2yk +.7zk z0 = 5. Also find formulas for yk and zk from A k = S kS 1 .

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QUESTION:

Find the limiting values of yk and k (k ) if yk+1 = .8yk +.3zk y0 = 0 zk+1 = .2yk +.7zk z0 = 5. Also find formulas for yk and zk from A k = S kS 1 .

ANSWER:

Step 1 of 2

Here we are given with matrix

The characteristic polynomial is given as

The eigenvalues are given by

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