A cycle (i iz is ... in) is called an n-cycle. If n 2 then the n-cycle is called transposition. Note that an n-cycle (i iz is ... in) can always be expressed as product of transpositions as follows (i, iz is ... in) = (i1 in)(in in-1)(n in-2) (i, i3)(i, i2). Write cach of the following as a product of transpositions. (a) (1 32 4) e S4. (b) (1 4 3)(2 5 6 7) e S7. (c) (143 6)(2 95 7 8) e Sy.

Q: Describe 3, 2, 1, 0, –1, –2, . .. | recursively. Include initial condition. аn — an-1 — 1, ај — 3 аn…

A: Given options are recurrence relation to the sequence 3,2,0,-1,-2..... By options we will verify…

Q: Calculate C(12,5) by hand. As C(n,r) = n!/(n-r)!r! identify n and r, and write out every number in…

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Q: 7 and N{B} 3 and N(A U B) = 10, how are If N{A} A and B related?

A: Given: NA=7, NB=3, NA∪B=10 We know that if NA+NB=NA∪B then there is no common element exist in Aand…

Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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Q: Calculate 1+ 2+3+…+ if n = 1, 2,…6 Calculate 1+ 3 + 5 …+ (2n - 1) if n =1, 2,…6

A: Apply the formula of sum of terms of an A.P with the first terms a, common difference d and the…

Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

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Q: From the list below, select all TRUE properties of determinants. (But do not select any false…

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Q: . By mathematical induction, prove that if ニ then A" =| 1 + 10n 4n -25 -25n 1- 10n 11 A - 9

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Q: In the following diagram below, what coordinate should point D be moved to make ABCD a…

A: Answer is following.

Q: (12 3 4) o (2 3 5 4 6) o (3 4 5 6) can be expressed as product of following disjoint cycles O None…

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Q: The net invoice price of a motorcycle is P 72,800.00. The discount was 20%. Find: A. net invoice…

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Q: The sum of the first n natural numbers, S = 1 + 2 + 3 + first n natural numbers is 171, determine…

A: Consider the given information:

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108. Find all…

A: All these problems can be solved using modular arithmetic. We presented the detailed solution in the…

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

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: i=n (5 + у;) (х; — 2) Зп + 2 i=1

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Q: Let Then where a11 = , a31 = , a12 = -1/9 , a32 = 1/9 1 +-679 A = 1 1 A-¹ = , a13 = 0 a11 a12 a13…

A: a11​=11782​ a12​=117−28​ a13​=11763​ a21​=1175​ a22​=117−4​ a23​=117−9​ a31​=117−13​ a32​=11713​…

Q: Suppose that |a| = 24. What is the generator of (a²l)n (a!o)? a20 a a14

A: Suppose that |a| = 24. We have to find the generator of <a21>∩<a10> .

Q: Q3. By using mathematical induction, show that 52n – 1 is divisible by 24, for all positive |…

A: We need to show that 52n-1 is divisible by 24. We can solve this using induction method.

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

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Q: Write the recursive definition for an = pn n! where a1 = p.

A: The recursive formula is used to describe the relationship between two terms of any sequence. The…

Q: 1a.) 0x**3  + 9x**3  1b.) 4X**3  - 9x**5  1c.) (3x   + 1x**3) + 2(9x**3 +(-3x)) 1d.)…

A: 1a.) 0x**3  + 9x**3 1b.) 4X**3  - 9x**5 1c.) (3x   + 1x**3) + 2(9x**3 +(-3x))1d.)…

Q: 2. If was written in the form ax then which of the following would be the product of a and n? (1) -…

A: To find: product of a and n if  5x4 was written in the form axn

Q: good 1. Ricky has a rubber shoes that he doesn't use anymore. It costs him P 3,273.00. If Ricky…

A: We can answer al the three question as below.

Q: Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n > 3, 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 an express an…

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Q: 1 (-i)ū

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Q: If an 6n – 8, list the first five terms of an. starting with n =1: {a1, a2, az, a4, a5}

A: This question is based on Arithmetic progression.

Q: 4 5 6 7 (8 4 3 2 7 6 1 5. 2 3 4 5 7 8 2 3 (1 11. Let a = 8 and ) 6 7 B = 5 2 1 6 4. (a) Write B as a…

A: Given permutations are. α=1234567884327615 β=1234567835278164 (a) To write β as a product of cycles.…

Q: Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A).

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Q: 6. 7, 0, -7, –14, . wwww Recursive: Explicit:

A: Given sequence,  7,0,-7,-14,... Which is a arithmetic sequence with common difference -7.…