Suppose a recurrence relation   an=an−1+20an−2 where a1=27 and a2=207   can be represented in explicit formula, either as: Formula 1: an=pxn+qnxnan=pxn+qnxn                                            or    Formula 2: an=pxn+qyn   where  x and y are roots of the characteristic equation.

Q: _If A = Verify that [A-!]" = [A"]¬1 ? l1 2.

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Q: Find the solution to this recursive relation an = an-1+3, a0=1

A: To Find the solution to this recursive relation an = an-1+3, a0=1

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Q: Let A [ - 5 13 12 13 2333 12 13 5 Explain why A-₁ = AT. -1 13

A: Step 1:

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: - 25х-1 dt 2*

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Q: The number ofunits in Z29[x] is 28 22 30 None

A: See the detailed solution below.

Q: Z

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Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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A: This problem can be considered as recurrence relation problem.

Q: Suppose A=| use Diagonalization to compute A" 10

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A: Introduction :

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Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

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Q: A = [12] 13 compute 4-3

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Q: Let i be a positive integer and A, = [-i+1,1]. Then U2, A

A: We have to use properties of union in this question.

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Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

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Q: 3 6. Let A= 0 x+1 1 x -8 x-1 For what values of x does A-¹ exist?

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Q: So what's the final value of x1 x2 x3 and x4? indivually

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Q: 5) Find NV ir ZN -- 20 7) Find DW if YW-4

A: Consider that the centroid divides the median in the ratio 2:1 (5) ZNNV=2120NV=21NV=202NV=10

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Q: Find the solution to this recursive relation an = an−1 − n, a0 = 4

A: Question: Find the solution to the recursive relation an=an-1-n,   a0=4