If a0 = 2, a1 = 3, and ak+1 = 3ak 2ak1, for all k 1, use methods of linear algebra to

Chapter 6, Problem 7

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QUESTION:

If a0 = 2, a1 = 3, and ak+1 = 3ak 2ak1, for all k 1, use methods of linear algebra to determine the formula for ak.

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QUESTION:

If a0 = 2, a1 = 3, and ak+1 = 3ak 2ak1, for all k 1, use methods of linear algebra to determine the formula for ak.

ANSWER:

Step 1 of 4

Given recurrence relation is

Prescribed initial conditions are

To find the formula for .

Let us define a vector by

Then,

Here,

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