An element x of a group satisfies x2 = e precisely when x = x-1. Use this observation to show how that a group of even order must contain an odd numder of elements of order 2.

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A: Y1 = 2x+2(x-7)Y2 = 3x-6

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Q: Solve the system of equations using augmented matrix methods x¹-2x²=-3 2x¹-x²=6

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Q: 4 201 Let A = -2 10 We want to determine if the equation Ax = 0 has nontrivial solutions. To do that…

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Q: -2 1 -1 2. Let A -2 0 4 1 5050 96 5 4 -61-2 9 1 -9 Find the rank A and the dim Nul A.

A: (2).rank A=3 and dim Null(A)=2Explanation:

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Q: Solve using augmented matrix methods  -4x¹-5x²=-3 -8x¹-10x²=1

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A: i have attached  one pic for answer and and one  explanation. Explanation:detailed explanation

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Q: 11.5.5. Let G = (Z/24Z, +). (a) Find a subgroup H of G that is isomorphic to (Z/4Z, +). How many…

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