Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 +an-2 – 5, express an in terms of n.

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

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Q: Find an expression for An, where n is an arbitrary positive integer.

A: Given: A=1423∈M2×2R

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Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

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Q: Find z-transfrm for (n-1) X(n) u(n-1) x (n) 5nucn) - 2 n (o.3) uci) 2)

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Q: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

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Q: 2. Let, a1 = 3 and for n 2 2, an = 2am-+1, express an in terms of n. 3. Let, a1 =3, a2 = 4 and for n…

A: Note:-Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: Prove the following statement: "Let a, b and n be integers. If n doesn't divide ab, then n doesn't…

A: The given statement is -" Let a.b and n are integers. If n doesn't divide ab, then n doesn't divide…

Q: Let, a1 = 3 and for n > 2, an = 2an-1+ 1, express an in terms of n.

A: a1 = 3 and, an = 2an-1 + 1 for, n≥2 We have to find the generalized term using the recursion…

Q: Show via proof that for two positive integers a, b where a 2 b, (use combinations e.g. n choose k)…

A: We shall prove for the given statement. Though it has little ambiguities.

Q: 2. Let, a1 = 3 and for n > 2, an 2an-1+1, express an in terms of n.

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: Express the following statement using N-notation.: 12.5 (3x + 4) for all real numbers x > 2. x + 2

A: In the given question the objective is to express the following statement using notation

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: Determine whether each statement below is true forn = 1, 2, and 3. Enter a comma-separated list of…

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Q: Find all possible values of P in x^2+10x+P=(x-A)(x-B) if P, A and B are all whole numbers

A: To find all possible values of P in x2+10x+P=(x-A)(x-B) if P,A and B are all whole numbers.

Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

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Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 – 5, express an in terms of n.

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + n², express an in terms of n.

A: In this question, we solve the recurrence relation  in terms of n an=2an-1+an-2+n2witha1=3a2=4

Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: Find the generalized union and intersection: 3) A = {1,2,3,...} A₂ = {x|x = 22m where m eset of…

A: Given that, Λ={1,2,3,…} Λλ=x|x=2λm where m∈set of integers from -λ to +λ The objective is to find…

Q: Suppose that J and K are points on the number line. If JK= 10 and K lies at 3, where could J be…

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Q: 1. Let, a1 = 7 and for n > 2, an = " express a, in terms of n.

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Q: Let ab be a two-digit number where a is the tens digit and b is the ones digit. Find the number of…

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Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: let a, b, and m be integer, prove that if 2a+3b>=12m+1, than a>=3m+1, or b>=2m+1

A: To prove: For integer a, b, and m if   2a+3b≥12m+1Than, either a≥3m+1, or b≥2m+1.

Q: Prove the following statement. ∀c ≥ 1 ∃d ≥ 1 ∀x ≥ d : c ≤ 3x. You may assume that c, d, and x are…

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Q: Suppose that A and B are two positive numbers and that x = In(A) and y = In(B). Write the following…

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Q: 4. Let, a = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2 +n, express a, in terms of n.

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Q: 3. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 + an-2 - 5, express an in terms of n.

A: We will solve the problem using recurrence relation

Q: For each positive integer n, show that и(п)и(n + 1)u(п + 2)u(n + 3) — 0

A: To prove : μ(n) μ(n+1) μ(n+2) μ(n+3) = 0  for each positive integer n.

Q: Let R = Z10 O Z100- (a) How many units does R have? (b) How many zero divisors does R have?

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 +n², express an in terms of n.

A: a1=3, a2=4 n≥3; an=2an-1+an-2+n2 First from the given, the given values shows that the terms are in…

Q: (b) {an}, where an 1 if n is odd and an = ; if n is even. |

A: Given that an where an=1n if n is odd and an=n2 if n is even.

Q: Suppose 671 + 3v2 – 203 = 0. - Let w = 301 – 6v2 – 403. Which of the following must be true?

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Q: 2. Show that if a is an integer other than 0, then a) 1 divides a h) a divides 0

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Q: For each integer n > 2, let P(n) bè thế för n-1 Eili +2) = n(n-1)(2n + 5) 6. %3D i=1

A: Given                   P(n):   ∑i=1n-1i(i+2)=nn-12n+56,          n≥2

Q: © Evaluate A2, where A = that al+bA + CA² = 0. 2 3 -5 5), and find a, b, c E R, not all zero, such

A: A = (2  -5)        (3   1)   A2 = (-11  -15)         (9      -14) aI +bA +cA2 = 0 ( a  0)   +  (2b…

Q: (b) If r23= 1, prove that R² (23) = 112=113 and 01.23 = 01 (1-12).

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Q: n Show that (") = (,“,) n-r.

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Q: 2. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + 5n, express an in terms of n.

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Q: For each integer n, let Tn = {n, n2}. How many elements are in each of T2, T3,and T1? Justify your…

A: Given that, Tn=n,n2. Substitute n=2 in Tn=n,n2  to find the number of elements in T2. T2=2,22=2,4…

Q: 2. Let, a, = 3, a2 = 4 and for n 2 3, an= 2an-1+ an-2 + 5, express a, in terms of n.

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Q: 3 and for n > 2, an = 2an-1+5, express an in terms of n. 1. Let, a1

A: The solution is given as

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: Assume that n(U)=70n(U)=70, n(A)=20n(A)=20, and n(B)=15n(B)=15. Then n((A∪B)′)=

A: The given details are                n(U) = 70                n(A) = 20                n(B) = 15

Q: For all integers a, b and c, if a divides b and a divides c, then a divides (4b - 3c). True False

A: Answer is TRUE

Q: Evaluate if possible a) 2 ∞ Σα η=4 n2+4n+3

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