Let G be a group. Then a mapping which associates to each element a € G, its inverse a-¹ is an automorphism of G if any only if G is abelian.

Q: 3) if Aza,i + a₂j + a³k , 13 = bi + bj + bk Prove that the .(A-B) -13 -(DXA) - A - (DXB) Vactors

A: We have to show Note: In the question  is given which is incorrect. It should be

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A: We have to solve the given differential equation.Concept/Formula required:

Q: Exercise 1.4.27 Find the rank of the following matrices. -5 - 16 -1 -4 3 6 5 12 122 0 -1 -4 -1 -2 1…

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A: Given, and

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Q: Solve for A. 5-2 23-8 -2 1 A = 01 -1/3 2 -38 -2/3 5 1

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Q: Exercise 3. Read the boxed definitions on p. 767. According to these definitions, how are the…

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Q: 1. What do the following pictures tell you about the value of H I ()+()*+G)*+G)*+... 2. What do the…

A: As per bartleby guidelines we solve only first question and rest question can be reposted…

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Q: If A = {2,4,6,8}, B = {6,7,8,9}, and C= {2,8}, then (BUC)\A= {7,9}. 3 If n = {3,4,5,...), then n³ −…

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Q: Q4/(B) Applying Newton's Raphson method to find the real root of f(x) = €¯³ - x

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Q: Consider the line L₁ described by r₁ (t) = (-t, 5+ 2t, 7 - 3t) and L₂ described by r₂(t) = (2+t,…

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Q: each part of this question, you are asked to give an example of something, and explain why is an…

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Q: 1. Let & be a connected category and hi Z→X and f Y. X= ง and g are Prove that if f ouch that f‡g,…

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Q: (a) Find the remainder of 21000 in division by 400. (Hint: We cannot use Euler's theorem directly…

A: As you said since 2 and 400 are not prime we cannot use Euler's theorem. However note that we…

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Q: Q2/(A) Using Laplacé transform, solve the following differential equation: y"-6y +9yte²t; y(0) = 0;…

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Q: he Big Ben clock in London has an hour hand that is 9.0 feet long and a minute hand that is 14 feet…

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Q: Dif(a1, a2): = d dt etaz a₂ +t) (etc t=a1 f(x, y) = ey+x, = (etª²a² + 1)|t=a₁ = eª¹ª²a² + 1.

A: Given a multivariate function:  The aim is to find .Partial Derivative: Derivate of  with respect to…

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Q: Use the fact that matrices A and B are row-equivalent.(a) Find the rank and nullity of A.(b) Find a…

A: As per our company guidelines we are advised to solve only the first three sub parts. Kindly repost…