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: HWGrouPA Prove the fallouwing identity. secA.SecB.CSCA.CSCB SectAtB) CSCA.CSCB-SecA. secB

A: sec(A+B)

Q: (3) Let 0 = 1234 6789 365 987 in S9 (a) Compute o2 and o (b) Write o as a product of disjoint cycles…

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

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Q: Which of the following is a monomial? OA. 20x - 14 OB. 11x2 OC. 20x9-7x OD. X

A: This question is related to monomials, we will solve it using given information.

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Q: 1. Write the following permutations in cycle notation. (1bd from 5.4) (1 2 3 4 5 (1 2 3 4 5 4 3 2 5/…

A: To find- Write the following permutations in cycle notation. 1234542513 1234514325

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Q: On Z+, a * b = aº ||

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Q: -2 1 -1 2. Let A -2 0 4 1 5050 96 5 4 -61-2 9 1 -9 Find the rank A and the dim Nul A.

A: (2).rank A=3 and dim Null(A)=2Explanation:

Q: nti Sacies

A: We apply the series method for following question

Q: Consider the following permutations in S9 1 2 3 4 5 6 7 8 9 (1 2 3 4 56 7 8 and r= 3. 5214 6. 9 78 5…

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Q: 2. List all elements of A = M₂ (Z₂). Give the units in A, as well as the zero divisors in A.

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Q: U(11) is cyclic generated by  Select one: a. 2 b. 10 c. 9 d. 5

A: Correct option a. 2

Q: 6.2 Which of the following groups are cyclic? a) Z12×Z, b) Z10x Zgs c) Z4xZ2sx Z, d) Z22XZ21 xZ6s

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Q: Exercise 8.6. Find permutations a, ße Sym(5) such that a² and 32 are the identity and the product aß…

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A: Let  Let Recall  the definition of Null  space  of  A.Null, null space of A. Using  the  above…

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Q: 4. Show that if ð > 2, then G contains a cycle.

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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…

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A: Given: Let f and g be disjoint cycles in Sn. To Prove that: fg = gf

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

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