2. Let o (1,2,3) (2,3,4,5). = (a) Write σ as a multiplication (b) Write o as a multiplication (c) Iso even or odd? of disjoint cycles. of transpositions.

Q: Suppose that {an} is defined recursively by: an = (an-1)² - 1 and that ao = 2. Find a2 and az.

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Q: If a = (4, 0, 4), b = (3, 4,-4), and c = (0, 4, 5), show that a x (b x c) = (a x b) x c. 60i + 96j -…

A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

Q: Write a = (1236)-'(435)(14) as a product of disjoint cycles.

A: A permutation is a bijection from a set to itself. The symmetric group of a set contains all the…

Q: Find the adjoint of the operation B = 2|0 × 1|- ; | 1 ×o |

A: This question asks to find the adjoint of the operation B^=2|0×1|-i|1×0|.

Q: Example 1.7.31. Evaluate 3i – 6 i=1

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Q: What does the symbol zα signify?

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Q: how do you write (14)(27)(523)(34)(1472) as a product of disjoint cycles

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Q: Solve the following ODE y +2y +y = x + e O a. (C1+ C2) e* + (x-2) + e /9 O b. (C1 + x C2) e* + (x-2)…

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Q: Express the composition (163)(254) ∘ (17246) in standard cycle notation.

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Q: 05. Write in sigma notation: 2 + 4 + 6 +8 + i-1 8 X2i =] 2i 22 i=0 0 16 i=2 + 16

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Q: (12 3 4) o (2 3 5 4 6) o (3 4 5 6) can be expressed as product of following disjoint cycles Select…

A: To express in disjoint cycles start from right and then go through left to right.

Q: 2 3 4 5 6 7 2 7 1 5 3 1

A: Here given permutation as 12345676271534

Q: (a) List the elements in A3 in lexicographical order, and list the elements in B3 in lexico-…

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Q: 1 2 and B ol: Compute the following: 2A, A – B, AB, and BA. Let A -3 1

A: Given problem:-

Q: How would you write this as a product of disjoint cycles?

A: LetWe have to write  as a product of disjoint cycles.

Q: 3. 09 0-16

A: Given determinant is : -1-263 To find the value of determinant.

Q: Let a = 55 38 (125) (1246). Write a³8 as a product of disjoint cycles.

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Q: Find A. A = = (2A)-1 1 1 || 4 [61] -4 11 6

A: Given  2A-1=6411 Inverse of a matrix X=abcd is given by  X-1=1ad-bcd-b-ca

Q: . Write (13)(1245)(13) and (24)(13456)(24) in disjoint c form. Give a simple description of how each…

A: Two permutations in product form are given.

Q: Let 4 1 - 3 -2 -9 and 1 A =| - 3 В C =| 0 3 Prove that 5 - 2 -1 1 1 – 4 | (BA)" – A" B" + AC = AC,…

A: (BA)T - ATBT + AC = AC In LHS, We know that, By the properties of Transpose, (BA)T = ATBT .…

Q: Find 312 i-0

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Q: Which of the following are multiplicative inverses:  (a) 5y/x and 5x/y (b) 5y and 7y (c) 7y/x and…

A: Here we have to find which of the options are multiplicative inverses.

Q: (Ъ) (1 4) 2) (1 3)(1

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Q: Give an example the illustrate each of the following properties: Commu- tative property of…

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Q: Y' = 2 (1+2) y' 2

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Q: e product (4 8 10 9)(2 7 6 11)(1 35 12)

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Q: find the laphece inverse S+3 fCH)- s* +3

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Q: 1 2 3 G ) as a cycle. Can Y Rewrite the permutation ( 3 2 12. one write the same cycle in many ways?…

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Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

A: Given: limx→3x3-27x2-9

Q: Let a = ( 1 2 3 4 5 6 :) 2 1 4 5 6 3 and 3 = 1 2 3 4 5 6 2 4 1 3 65 (a) Find a B(2). Find 6-¹(2). ο…

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Q: If P(A)= 0.7 and P( B)= 0.6, find P (AUB) if: A and B are where Be is complement of B (not B)…

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Q: Let :[6.-5] and = [-1,5). Find the vecror %3D 7 =62-55 and its additive in verse

A: Given that: x→=[6,-5] and y→=[-1,-5]

Q: A=[1 -3 -5 -8]      [0 5 -5 -6]      [0 0 -4 -5]      [0 0 0 4] Inverse of the following matrice

A: use the concept of  A = IA

Q: g mall, restaurant c

A: Given, in certain shopping mall, restaurant charges are  125 150 200 165 175 190 230 180