This exercise provides an alternative to Theorem 8.2 for factoring an r-cycle into transpositions. Prove that (x1, X2, X3, ..., X,) =(x1, x2) • (x2, x3) • (x3, x4) • • • (x,2 Xr-1)• (X-1, *,). O ...O

Q: Prove that Ją (2) = =- J¼ (2) – J_4 (=)

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Q: 6. (a). [3-2 စာ ၅၊ = Let A 1-1-2 = 0-2 Compute A-1 ***** (b) Use part a) to fin all solutions to the…

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Q: 2) Show that 2m +1 m P(x) m +1 -xP (x) m+1 (x)F

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Q: Evaluate z' if z = [1 + (x² − 1)³] ²³ O a. 2(2²-1)² (1+(2²_1)²³) i O b. none of these О с 41(2²-1)²…

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Q: (5) The ring (Z6, +6,•6 ) has that rad Z, (a) ((0), +6.-6 )

A: Given: To explain the correct option of the given statement as follows,

Q: 20. Solve for the Wronskian of the set of functions: 3x - 1, x* - 2. 2x + 3 A. 4x (9x + 10x-90x -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: U(5) is not isomorphic to U(10) اختر احدى الدجابات True False

A: U(5)=1, 2, 3, 4U(10)=1, 3, 7, 9

Q: If Z ~ N(0,1), compute P(Z2 < 3)

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Q: Find the coefficient of X^35 in the generating function (x^4+x^5+x^6+x^7+x^8)^5 (Show work and…

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Q: 2 Show that for n>o Ê i=0 (-1) ( ^^ ) = 0

A: We have to show

Q: compute η2

A: η2  is given by : η2=SSbetweenSStotal

Q: 14. Suppose that Yk+2 – Yk+1 + 2yk = 4*, k > 0, and that yo = 2, y1 = 1. Find yk using the method of…

A: Solution of difference equation is a function that satisfies the given difference equation. Solution…

Q: Compute P(X1 + 2X2 − 2X3 > 7) if X1, X2, X3 are iid with commondistribution N(1, 4).

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Q: n 5. Let n be a fixed positive integer. Denote by Po the set of all real polynomials of degree n or…

A: A nonempty set V together with two operations - vector addition and scalar multiplication is called…

Q: If In x +In(x-3)=In(6x), then X=

A: The equation is given as ln x+ln x-3=ln 6x

Q: Show that det [1 1 0 0 1 1 0 0 1 0... 0 0 1 ⠀ ... 0000 1000... 00 00 11 0 1 = 1+ (-1)"+¹.

A: As per the question we are given a matrix determinant, whose all diagonal and super-diagonal…

Q: IF fx) = (1 - x) and g(x) = 9 - x, find fg(x)) and g(fx)). Ag(x)) = 9(Ax)) =

A: Given that:           f(x)=(1-x)2 and g(x)=9-x Find f(g(x)) and g(f(x)).

Q: 10) In (x – 6) + In (x + 1) = In (x - 15) %3D

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Q: (Book: 7-25) Show that if b→b and E{X-bF)→0, then X→b in MS sense as n→∞.

A: The given of the problem is that bn approaches b, and the expected value of the absolute value of…

Q: Find the state-space form of the following mathematical model x₁ +2(x₁ - x3)-2(x₂ − x₂ ) - ² (x₂-x₁)…

A: Given Information:The system of equation is given as:To find:The state-space form of the system as…

Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: 6. (6x – 15)' (2r+ 1)

A: To find x ?

Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: (1 2 3 4 5 6 7 \3 4 5 2 7 5 6 E Sz is a product of -------- 2-cycles. a = O 2 Оз 4 O 5

A: .

Q: -5= =DS"S"?{(m-3)x²+³"(m - m x- ? y)'-4myx] dydx

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Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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Q: 5. Find LU Factorizatioon of A = [5 2 1 1 3 2 7 1 2 3 2 1- Show the work!

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Q: 9. Compute s² (s-3)(s+4)(s-1) (3-1) (0).

A: Formula used Given

Q: We want to find the number of ways in which 3r balls can be selected from 2r red balls and 2r blue…

A: We have , 2r red balls and 2r blue balls . To find : the number of ways in which 3r balls can be…

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: Q.5 Find all entine functipns a with

A: Given: The given function is fz≤zez

Q: Prove that (+¹)=()+(²1).

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Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

A: Answer

Q: S' = 4 + ( 20 ) * + ( ਲੰਡਨ ) * ( ) 1 + 2022 * 1 + 2021 2 2 + ... + 1+ + 1+ ² 2021 2020 1+ Find S = ?…

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Q: Example 6-44. Show that eitr = 1 + (eit – 1) x(1) + (e# – 1)2 ) + + (eit – 1y. where x =x (x – 1) (r…

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Q: 4. Let X1, ,X4 be iid Unif(0, 0). (a) Show that X(4) is independent of X(1)/X(4). (b) Show that X(4)…

A: Given that X1,X2.............,X4 be iid Unif0,θ (a) X4 is complete sufficient statistics and…

Q: state formally the Heine-Borel Theorem in R^k

A: Let S be a subset of ℝk. Then the Heine-Borel theorem states :

Q: Let 1 -1 8 -3 -5 2 -1 , and B = 1 %3D %3D -2 1 4 -7 Compute A-1, (BT)-1 and B-1A-1. What do you…

A: A=1-1102-1-213, B=8-3-50124-76 Expanding the determinant of A, B along column first…

Q: If A is an adjoint operator on H=K2 and  for x=(x(1), x(2)), we define A(x)=(x(1)-x(2), x(1)+x(2)),…

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Q: Prove that x=0(x)

A: We say that a function f is O(g) if there exist constants M and C&gt;0 such that For all x&gt;M…

Q: 7. The quadratic spline interpolating (-1, 0), (0, 1) and (1, 3) is Qo(x) = 1 + 2x + x², Q₁(x) = 2x…

A: