Consider the following permutations. 1 Symmetric group 11 (1 cycles. 1 2 3 4 5 6 5 3 2 6 14 b) Calculate expressing 1 2 56 of a) Express of disjoint cycles. each Calculate each 56 and 3456 1 3 the १ b - a and T orders g TOT. and T from the and TOT, products of disjoint each as products O of the elements ə

Q: 14. Let A = {1,2,3,4,5,6} and p₁ = (4,2,5) and p₂ = (2,6,1) be permutations of A. Compute p₂¹P₁-1…

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Q: (i) Write the following permutations in S9 as a product of disjoint cycles 1 2 3 4 7 298 5 6 7 8 9…

A: Given  f  can be written as a product of disjoint cycles as                 f = (1  7) (3  9  5) (4…

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Q: 4. Bijections and Permutations: a. Let t= 263198475 in one-line notation. Give two-line notation and…

A: (a) let τ=263198475  claim- give two line notation and cycle notation. then its inverse, square in…

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A: In △ABC, b = 30∠A = 30°AB = BC = x (assume) To evaluate: The value of x

Q: Consider the product of cycles (1 2)(4 7 8)(2 1)(7 2 8 1 5) that are permutations of {1, 2, 3, 4, 5,…

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Q: Write the conjugate of va + 3

A: Definition of conjugate.

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Q: 6. How many distinct cosets are there in the factor ring Z[i] /3+i)? Explain your answer.

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Q: Reduce to Canonical form Ur + 5 Ury + 6 uyy = 0 None UgE = 0 Uen = 0 = 0

A: compare the given equation with Auxx+Buxy+Cuyy+Dux+Euy+Fu=G therefore, A=1,B=5,C=6 find B2-4AC…

Q: 1. 2. (1 2 3 4 5 6 7 4 5 1 7 8 Let a = 2 3 Write aß as products of disjoint cycles. A. (13746285) B.…

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Q: Question 1. State whether True or False. Provide a reason in each case. a. The pair (No, +)…

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Q: dT -k(T - 35), where k is a positive constant. dt

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Q: 4. Convert (101001000)2 from binary to decimal notation and (1984)j10 from decimal to binary…

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Q: nti Sacies

A: We apply the series method for following question

Q: 8. Give a "train-theoretic" proof of the Fibonacci identity: U11 = u4 · U6 +u5 · U7.

A: Given, u11=u4·u6+u5·u7 Where ui represented the Fibonacci numbers. For train theoretic proof of the…

Q: 2. Find the following elements in Z₁9: a. 13 X19 17 b. 13 +19 17 c. -12 (the additive inverse of…

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Q: If 3 1 0 A = | 5 2 -1 1 4 - 2 The adjoint of A is -1 1 9 9. 18 - 6 3 -11 – 11 1 True False

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Q: Matrix with rank A= 4 het A be a 5x6 ind cim Row A, dim Col A, dim Nul A, din Bow AT, dim Cal AT,…

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Q: 1. Write (2 + i) (4 - 3- 21 in the form a bi, where a,bR.

A: Value of i 2 = - 1 And i 3 = i   ( a - b ) 3 = a3 - b3 - 3 ab ( a - b )

Q: 2 345 6 7 1/ 168 LEt a= 2. 1. 3457 a)Write a as a product of disjoint cycles. b) write a as a…

A: First we have to write alpha as a product of disjoint cycles-

Q: Question 2 (Cyc Given positive integers a1, a2, ...,ak with a1 + a2 +...+ ag = n, how many…

A: Given that there are a1,a2,...,ak positive integers. Also a1+a2+...+ak=n. Without loss of generality…

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A: Permutations and combinations are two methods in mathematics. Permutation deals with arrangements…

Q: Is (S.) a group? C a a b с b b b с с с

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Q: 1. Which of the following statements is NOT true on operations on real numbers?  a. Addition is…

A: let a,b,c∈Rwhere R is the set of real numbersand * denotes the arithmetic operation.commutative…

Q: 2. Find the LU factorizations of and 20 5 2 -6 3 -13 -3 4 9 16 17 2 4 -6 2 13 9 دن و ان 5 4

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Q: a) Find a generating set of U(20) with two elements. b) Use the generators you found in part (a) and…

A: The set of integers modulo n defined by Un=k:gcdk,n=1 The set Un is a group under multiplication…

Q: 14. Consider the permutations a = (5 21 4 3), B = (1 3)(2 4 6), y = (12 4)(3 5 6) of {1,2, 3, 4, 5,…

A: Which of the following is correct

Q: 1. Define the multiplication operation as modulo 10 in G = {2,4,6.8}. Determine whether the system…

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