Prove that (1234) is not the product of 3-cycles.  Generalize.

Q: Find the length of the func tion based Vange de fincd belouw: the on 10<x <29 10

A: We have to find the length of the given function in the range 10 ≤ x ≤ 29. y = 110ex+e-9x

Q: If (ab) and (cd) are distinct 2-cycles in Sn, prove that (ab) and (cd)commute if and only if they…

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Q: Find all ideals of Z3 [i] . Show your work. (-

A: ℤ3i is clearly a field  because ℤpi is a field if p≡3 (mod 4). Thus 3≡3(mod 4) therefore ℤ3i is a…

Q: Find the QR decomposition and prove -3 -5.

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Q: Label eachof the following statement/s as either true or false.   Every permutation can be expressed…

A: Every permutation can be expressed as a product of disjoint cycles.

Q: Write the permutation corresponding to R90 in the left regular representationof D4 in cycle form.

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Q: If A²=0, prove that A cannot be invertible.

A: Given,If A²=0, prove that A cannot be invertible.

Q: The zero-product principle states that if AB = 0, then________.

A: Zero-product principal:

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A: Suppose we have L shaped tiles Prove that for all n&gt;=1 it's possible to lay these tiles down to…

Q: Suppose A=| use Diagonalization to compute A" 10

A: In the given question we have to find the 10th power of the matrix A s.t A=10-12. Concept: If a…

Q: If n=3, expand µ = a"x¡x¡

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Q: If all the cofactors are zero, how do you know that A has no inverse? If none of the cofactors are…

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Q: Prove that the equation x+5x=4cosx cannot have more than one real ro

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Q: a) Is a G = Z24 cyclic? Why %3D

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

Q: PROVE that 2a + b = 0.

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Q: Find all the generators of Z24-

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Q: I have to identify the recursive and explicit rule. I need to select two

A: Answer: Option F f(n)=f(n-1) . r Option A f(n)=3. 4n-1

Q: Show that U(8) is not isomorphic to U(10).

A: To Show: U(8) is not isomorphic to U(10)

Q: Show that the power set of 2, 2º, is algebra on 2. an

A: A σ-algebra is a type of algebra so, every sigma algebra is an algebra.        (1)

Q: Let P3 have the inner product

A: Given, pt=t2 and qt=2t-3. given by evaluation -2,-1,0,1, and 2. p-2=4q-2=-4-3=-7 p-1=1q-1=-2-3=-5…

Q: The zero-product principle states that if AB 0, then

A: If AB = 0Then zero-product principle states that this is possible only if - A = 0andB = 0

Q: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

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Q: Prove that Z[√ -2] and Z[√ 2] are unique factorization domains.

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Q: Show that U(8) is isomorphic to U(12).

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Q: Show that (an) is increasing

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Q: Prove that the order of a k-cycle in S, is k.

A: Suppose σ is a k-cycle in the group Sn. then we follow that σ is a permutation of length k in which…

Q: Show that Z4 is not isomorphic to U(12) by comparing the orders of elements.

A: z4=0,1,2,3 is group w.r to +order of elementsoa=n⇒an=e where n is least positive…

Q: Find the orders of all the elements of Ag.

A: A8 is the group of all even permutation of S8.

Q: 7. Determine whether g(r) =5 6x even, odd or neither. Discuss its symmetry. -

A: f(x) = f(-x), then f(x) is even function,  f(x) not equal to f(-x), then f(x) is odd function.

Q: write down in sequence the (teps in using the Cramer's ( application s peterminants). Rule OF

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Q: Prove

A: To prove  tanxcosec2x-tanxsinxtanx+cosx=cos2xcosecx

Q: (1) For each member of your group record their response to: Give an example of a polynomial and an…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find all the conjugacy classes of D4.

A: We have to find conjugacy Classes of the Dihedral Group, D4

Q: 1- Show that : is R- module .

A: Note that, in the above definition of Modules, we used the concept of left R - Module &amp; right R…

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

A: We need to prove that δ≥2 , then G contains a cycle , Asume that G is a finite graph, Let V1 ∈ G,…

Q: Prove that 8x3 - 6x - 1 is irreducible over Q.

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Q: Is Z6 a subring of Z12?

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Q: Prove the

A: Follow the steps that I listed given below pitcher.

Q: Produce an example of a subset of 1R³ that is Closed under addition, but not closed under scalar…

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Q: What are all of the distinct generators of Z17 with respect to multiplication? What are all the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the ordinary generating function for the sequence 0,0,0,0,1,1,1...(Hint: it is not a…

A: We need to find an ordinary generating function. The sequence is 0,0,0,0,1,1,1,.... Consider:…

Q: Show that for A and B of n×n order with complex enteries the matric Ab need not be similar to BA ,…

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Q: Prove that gcd(a + b, a - b) = gcd(2a, a – b) = gcd(a + b, 2b). Show your work! Justify each step.

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Q: Find the fnckion below the inverse of %3D

A: given function is                                                      y=x2+4 we have to find…

Q: 6x-C), Prove that If2zf(x+ct)+Ø て

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Q: Express x8-x as a product of irreducibles over Z2

A: We have to express x8-x as a product of irreducible over Z2. Definition:- Irreducibility is defined…

Q: (a) Prove that the product of two even permutations is even.

A: please post the multiple question separately. Here I answered 1st question only as per our policy.