For G being each of the following groups, compute the centre Z(G): (a) S3 (b)Z/3Z x S3

Q: The transformation T: R² → R², which maps the graph of y=-√2x+1-3 onto the graph of y=√x, has rule…

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Q: a b - Let H = 5, d E R, ad 0 Is H a normal sub- group of GL(2, R)?

A: Given: H=ab0d  a, b, d∈ℝ, ad≠0. We have to check whether H is a normal subgroup of GL2, ℝ or not.

Q: (b) Find the order of the group: Z(A) = {X € GL₂ (Z7) | AX = XA} where A = (11).

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Q: Given that S is the triangle with vertices (-5,5), (-5, -5), and (5,-5), determine whether the…

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Q: 3. Let Dn (n ≥ 3) be the dihedral group of order 2n. (i) Show that D10 ≈ D5 × Z2 by constructing an…

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Q: 2. Let G be the group of 2 x 2 matrices under addition and H = {(ab): a +d=0}. Prove that H is a…

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Q: Consider the groups (R,+) and (R x R. +). Define the map Rx (RX R) → Rx R defined by ra (z. y) =…

A: The given groups are ℝ, + and ℝ×ℝ, +. The map ↦: ℝ×ℝ×ℝ→ℝ×ℝ is defined as, r↦x, y=x+ry, y Definition:…

Q: Determine which of the following transformations are linear transformations. O A. The transformation…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let T₁: R5 R³ and T₂: R³ R² be linear maps. What are the possible dimensions for the kernel of T₂?…

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Q: Let G be the group with presentation (x,y: 1² = 1, r² = y²₁ xy = y ¹). Decide how many elements are…

A: Consider the given group G with presentation, x,y:x4=1, x2=y2, xy=yx-1 it can be observed that it is…

Q: Find the transformation R (x) for x= .a O R,(3)=L 3. None of these b O .c O R, (x) =| .d O R, (x) =

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Q: unctions are well-defined group homomorphisms? Se elections; you cannot score less than 0 on this…

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Q: (3) Conjugate the map f(x) = 2x² +x – 3 to a map of the form Q(x) = x² + c. Find the conjugacy map h…

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Q: Construct a linear fractional transformation that takes the given points z T(z) = and 23 Z₁ Z₂₁ Z₁ =…

A: A linear fractional transformation takes the points A linear fractional transformation takes the…

Q: 5. Let T: P₂ (R) → P₂ (R) be defined as P(ax² +bx+c)=((2a − b)x² + (3a + 3c)x+ (a − 2b - 3c)). Find…

A: 5. Given that T:P2ℝ→P2ℝ be defined as Tax2+bx+c=2a-bx2+3a+3cx+a-2b-3c. We have to find the KerT and…

Q: For the transformation T : M2x2(R) → P2 given by T |º| = (a+2b)x² + (b+3c)x+c+4d find the following:…

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Q: Let G = 64. (a.) Let a = (123) (14). Write a ¹2 in disjoint cycle form. (b.) Consider the subgroup H…

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Q: Consider the map: n+1 = f(xn). If ƒ(ƒ(ƒ(ƒ(ƒ(x))))) − x = 0, which statement below is unequivocally…

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Q: Suppose 0: G-→ G be a homomorphism of groups. Show that: (i) Kere is normal in G (ii) The mappping…

A: Normal subgroup: A subgroup N of a group G is said to be a normal subgroup of G if  gNg-1=N , for…

Q: Let x= and u then find the transformation P.(x). 3/5 4/5 [2/5] 4/5

A: Given x=5-5 and u=34

Q: For each of the following linear operators on R2, find the matrix representation of the…

A: For given linear operators on R2 We have to find the matrix representation for the transformation…

Q: The group of all rotations in space that preserve a given cube has order: (u) 6. (b) 12. (c) 8. (d)…

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Q: Suppose G| = 170, PE Syls(G), and QE Sylı7(G). %3D (i) Calculate ns(G) and n17(G). (ii) Is P4G and…

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Q: Determine the piecewise representation of f(x) below: f(x) = |x2 - 14x + 48| Equation A if Condition…

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Q: 2. Let G = (1, 0). Decide if G is a group with respect to the operation * defined as follows: x * Y…

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Q: Determine an affine transformation T that maps the large figure to the similar (smaller) figure. The…

A: From the figure, the transformed figure is shrinking and translated from the origin. The left side…

Q: (a) Let eg be the identity element of G, let e be the identity element of H, and let g E G. Prove…

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Q: Given f(x)= |x| and g(x) is a transformation of f(x). Find the function g(x) from the following…

A: The first function is f(x) = x.The graph of f(x) is

Q: (c) Suppose that G = (a), a e, and a5 = e. Construct a Cayley table for the group (G,.). CIG [11

A: We shall answer first question only as you have asked more than one different question. For others…

Q: Use the superposition principal to draw a graph of each. Please graph a), b) and c) separately. a)…

A: The superposition principle, also known as superposition property, states that, for all linear…

Q: G TE B D E Find the order of the subgroup generated by a for each of the following groups: (124)…

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Q: Determine an affine transformation T that maps the large figure to the similar (smaller) figure. The…

A: The coordinates of the figures are given by