If H is a normal subgroup of G and ∣H∣=2, prove that H is contained in the center of G. Determine all normal subgroups of Dn​ of order 2.

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Q: 2d

A: Definition of P2​(R): Space of polynomials of degree at most 2 with real coefficients.Introduction…

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A: Graph 1: NoGraph 2: NoGraph 3: NoGraph 4: YesGraph 5: YesGraph 6: No Explanation:Recall that the…

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A: The General form of a parabola is given by  where (h,k) is the vertex of the parabola.The vertex of…

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A: The objective of the question is to prove that the given function f : S_n → A_{n+2} is injective. An…

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A: Average rate of change = 1 Explanation: Given that, f(x)=3x2−2x+1 we have to find the average rate…

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A: Ans:(d) (Z4, .).For details please see the explanation.If you have any problem then let me know in…

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Q: (3 marks) Let r Є R and u = v ■- (2) - (+) w- () (+), -4 " W = For which values r = R is the set {u,…

A: The vectors are linearly independent for all r except 1. Explanation:

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A: Therefore, the required answers are a) option iii) A=x2+x2000​b) x=10c) A has a local minima at…

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A: Please refer below page.If you have any doubts please feel free to ask.Explanation:Step 1: Step 2:…

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A: Given We have to find

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A: The objective of this question is to find out the number of different collections of 6 books that…

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Q: Identify the row matrix. Matrix C What is its transpose? ✔is a row matrix.

A: given row matrix C=

Q: Question for math. If L varies directly as h, and L=56 when h=7, find L when h=3.

A: L varies directly as h, and L=56 when h=7, find L when h=3.

Q: Question 4 2 pts Which one of the following columns is correct for the truth table (p-> ~q), where p…

A: Truth table: p→∼qpqp→∼qTTFTFTFTTFFT Explanation:Option 1 is the correct answer for the truth table…

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A: SolutionRadius(r)=3 inCircumference (c)=18.84 in

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Q: Find the determinant of the matrix 3 5 -1 0 -3 0 -2 4 determinant =

A: The given matrix

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A: The objective of this question is to determine the cubic function A that passes through the points…

Q: 16) (5√√5-3)(-4√√5+4)

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Q: 1 1 Let A = = 2 -1 1],μεR. 4 a) (4 marks) For each µ Є R find Cartesian equations for Col(A) and…

A: a. For each value of μ ∈ ℝ:1. If μ ≠ 3, the Cartesian equations for Col(A) are all of ℝ³, and the…

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A: Given . We have to prove

Q: Consider the following two systems. (a) (b) 3x+5y -2x + 3y || || = -1 2 3x+5y -2x + 3y 1 = -4 (i)…

A: We solve the given problem using the concept of inverse.

Q: 13.25

A: The objective of the question is to find the values of the unknown constants that make the matrix A…

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A: Explanation is given below:Explanation:

Q: 7. The characteristic equation for square matrix A is the equation det (A-AI)=0. The scalars that…

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Q: Consider the vectors a = (3,0, -4), b = (4, 5, 3), c = (0, 1, 0) € R^3. Find the angle between b and…

A: Angle =4π​ Or45°Area = 5 square unitVolume = 7 cubic unit Explanation:

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A: The objective of the question is to find the number that needs to be added to the quadratic equation…

Q: Question 3. Please solve this and show steps. Thanks.

A: C option is the right answer. Determinant is zero (0)Explanation:The method employed in the…

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A: The objective of this question is to define what matrices are and provide examples of them.

Q: In Exercises 7-10, find A2, A-2, and A-* (where k is any inte- ger) by inspection. 9. A = ○ 13○ 12 0…

A: To find  (where k is any integer) by inspection.

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A: Please find the attachment for the graph.Explanation:

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A: The given graph