a b (88) 0 d Let G be the set of all 2 × 2 matrices under matrix multiplication. Is G abelian? where ad 0. Prove that G forms a group

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A: Given, N(t)=P(t) + L(t) +S(t) + Q(t)  Solution to part 1: We know that if Z(t) = X(t) + Y(t),then…

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A:

Q: 2. The value of f¹dx = ..., for each Chebyshev polynomial T, (x), n ≥ 0. dx=, √1-x² c) 0 d) None of…

A: For each chebyshev polynomial we have

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Q: 800 = 1 * Bind E [2x²-1) and E[(x-13] Q23 Given ap.m.f. fox)= for X=1,2,3,4 30

A: Given,PMF  f(x)=x10 for x=1, 2, 3, 4 and 0 otherwise.First, We will find the expectation of the…

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A: Given,         x'=400-595004x

Q: 9. Prove that if G is a group of order 60 with no non-trivial normal subgroups, then G has no…

A:

Q: 2. If f(x) is an even function and g(x) is odd function, then a) f(x) g(x) is an function. b) f(x)…

A: Solution:-

Q: (a) Find the Fourier series of the 2π-periodic function f(x) = x² in - π < x < 1. -2<x<2 else a, (b)…

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Q: Which of the following is NOT a circuit in the graph? B E F D CC OABFEA OBFDCB O None of the Above

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A: Introduction: The Shell Method is used to calculate volume by breaking down a solid of revolution…

Q: 1. Suppose £5000 is invested for five years. Calculate the amount accumulated at the end of five…

A: As per the guidelines i had solved the first questions kindly post another questions separately.

Q: 4. Prove that a permutation matrix is orthogonal.

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Q: (a) Prove the convergence or divergence of each of the following series: 1! +a! +3! + +n! 20+1 2+1 6…

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

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Q: Describe matrix multiplication of two matrices A and B in terms of linear functionals (the linear…

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Q: 7. Suppose that Professors Wells and Zeddes have final exam scores that are approximately normally…

A: mean μ=75 standard deviation of wells scores σW=10 standard deviation of zeddes scores σZ=10 a) with…

Q: 1 Let f(z) = ((z -3i)² + 9)ez-3¹. Evaluate f f(z)dz, where C is |z − 2i| = 2, positively directed.…

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Q: The table below presents the real wage and nominal wage of non-agriculture workers in the…

A: Given: The following table presenting the real wage and nominal wage of non-agricultural workers in…

Q: بال 20 S 3y م + dx dy

A: The double quintessential is maximum typically used to calculate the floor vicinity of a…

Q: 2. The value of ¹₁ KIN [Tn (x)]² √1-x² 5 LEIN dx = ..., for each Chebyshev polynomial Tn(x), n ≥ 0.…

A: The given integral is                                    ∫-11Tn(x)21-x2dx where Tn(x) , n≥0, are…

Q: S- A solid consist of a cone of aradius r and height hi and a cylinder of radius r and height h₂.…

A: Use the following formulae, to obtain the solution. Volume of Cone=13πr2hVolume of Cylinder=πr2h…

Q: 1. What is the value of the correlation between Academic Performance and Digital Literacy? A.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 0) Any u unit vector and each (a, b) for the point, D_ƒ (a, b) = − D₁ƒ(a,b) True False

A: In this question, the concept of Directional derivatives is applied. According to the Definition of…

Q: 6. Let a1, a2,...,an be distinct positive in not containing s = a₁ + a₂ + + an. A grassh A AL icht…

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Q: 7 (b) On the floor of stock exchange traders meet to buy and sell stocks of various companies.…

A: Given: y'=ty To find: y

Q: 3.5.13. Given n = N, let pn(t) = t" for t = [0, 1]. Prove that the sequence {Pn}neN converges…

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Q: X If A(x) = f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A:

Q: Side-Angle-Side?

A: Given,          To  prove that,             ∆LMK≅∆NMK   Side-Angles-Side

Q: 4. -15 -10 (-4,4) (-4, 3) -5 (-4,-5) -4,-6) -10- 0 -5- --10- --15- 5

A: The standard form of the equation of hyperbola with center (h, k) and transverse axis parallel to…

Q: Prove that = z² +E=o(-1)" (n + 1) (²22)", where |z-21 < 2. 4

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Q: b) Solve the following second order differential equation, clearly showing all calculation steps dy…

A: To solve the given second order differential equation :-

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A: Given,   x 0 1 2 3 4 y 1 1 9 61 205

Q: (b) Let g(x)=√x with domain {x|x>0}, and let e > 0 be given. For each c > 0, show that there exists…

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Q: +∞ η=1 Σ 4η (n+1)3

A: The solution is given as

Q: Given: z = 6(cos30° + isin30°), find 3. z³

A: Given the complex function

Q: 2. Find the LU factorization of the following matrices without pivoting 1 2 3 a) A = 2 5 4 354 1 -1…

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Q: Q2) Let(M₂ (R), +..) be a ring. Prove H = {(a) la, b, c = R}is a subring of (M₂ (R), +,.).

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Q: Suppose that Charles Barkley has $25000 to spend on the repair of a gravel driveway. He wants to…

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Q: The number of zeros of sin() is: a) 1 b) Infinity c) 2 d) 4

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: •4.0.5 f Determine area the top and all side of a platform below. Note// Parallogram shape 6m -2.65m…

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Q: Solve the ordinary differential equation y'+4y-3x³, using Runge-Kutta method with Xo-0. Yo-1, X₂-2,…

A: Solution: Given, y'=3x3-4yy(0)=1h=0.5y(2)=? Using formula , k2=hf(x0+h,y0+k1) Second order R-K…

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Q: Find the volume of the paraboloid, z = 9 - x² - y², that lies inside the cylinder x² + y² = 4.

A: It is seen that the paraboloid and cylinder both are extended upto negetive infinity of along z…

Q: d) Locate and identify the stationary points in the function y = x³ - 4x² + 2x

A: Finding stationary points

Q: Find the volume of the region cut from the solid sphere

A: Given the region cut from the solid sphere x2+y2+z2≤4a2by the cylinder x2+y2=a2.