If a0 = 0, a1 = a2 = 1, and ak+1 = 2ak + ak1 2ak2 for k 2, use methods of linear algebra

Chapter 6, Problem 11

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QUESTION:

If \(a_{0}=0, a_{1}=a_{2}=1\), and \(a_{k+1}=2 a_{k}+a_{k-1}-2 a_{k-2} \text { for } k \geq 2\), use methods of linear algebra to determine the formula for \(a_k\).

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QUESTION:

If \(a_{0}=0, a_{1}=a_{2}=1\), and \(a_{k+1}=2 a_{k}+a_{k-1}-2 a_{k-2} \text { for } k \geq 2\), use methods of linear algebra to determine the formula for \(a_k\).

ANSWER:

Step 1 of 3

Given that  , and .

The aim is to find .

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