Let G act by conjugation on G. (a) Fix g ∈ G. Describe, as precisely as possible, the stabilizer of g under the action of conjugation. (b) Describe, as precisely as possible, the kernel of the action of conjugation.

Q: heck if the linear transformation T : R3 → P2, T(a, b, c) = (a + b + c) + (a + 2b +c)x + (a + 2c)x2…

A: Isomorphism of a transformation: A map f:V→W that is an isomorphism between two vector spaces V and…

Q: (a) Define the T1-space.

A: Define the T1 - space

Q: Let G be a direct product of H and K then Z(G) is a direct product of Z(H) and Z(K).

A: By the set inequality i have solved the problem

Q: Prove the zero transformation is not invertible

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Q: Which are invertible

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Q: Are the relations represented by the following matrices equivalence relations? 1 0 1 0 0 10 1 10 10…

A: Introduction: Every relation has a matrix representation. When the diagonal entries of the matrix is…

Q: (b) Consider f(x) = 2x³ + 3x² + 4 in Z[], and the evaluation homomorphism 2 [2] : Z₁ [2] → Zg. (i)…

A:

Q: Let R= {(a, b): 3keza k* b} be a relation over the positive integers. Prove or disprove thatR is a…

A: A relation R is partial order relation if R is reflexive, antisymmetric and transitive.

Q: b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an…

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Q: (c) Prove that the adjoint of a compact operator is compact.

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Q: Let f be the function from {a, b, c} to {1, 2, 3} such that f (a) = 2, f (b) = 3, and f (c) = 1. Is…

A:

Q: Let A = 1 -X -X X 1 -x X X -1 Find x such that A is invertible.

A:

Q: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab > 0

Q: Let T: P₂ P₂ be a mapping defined by T(a + a₁x + a₂x²) = ao + a₁ (x + 1) + a₂(x + 1)². a) Determine…

A:

Q: (5) Let ƒ : A → B and g : B → C, where f and g are functions and A, B, and C are sets. (a) Prove…

A: In 2 nd part construct a function

Q: is bijection. Do the same thing with Z,.

A:

Q: Define the linear transformation T by T(x) = Ax. Find (a) the kernel of T and (b) the range of T.

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Q: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

Q: Show that if G is self dual, then |E(G)| = 2|V(G)| – 2.

A: Definition (Self-dual): A graph G is said to be self-dual if there is a graph isomorphism between G…

Q: {(a,b, c)/b=a+c} defined on Z×Z×Z,where Z be the set (d) List five elements of the ternary relation…

A: Note:  For (d), We need to list five elements of the ternary relation S = {(a, b, c)| b = a+c}…

Q: Show that U(8) is not isomorphic to U(10).

A: To Show: U(8) is not isomorphic to U(10)

Q: Let A = {0, 1, 2, 3), and dene a relation R on A as follows: R = {(0, 2), (0, 3), (2, 0), (2, 1) }…

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Q: Let R be the relation on the set A = {a1, a2, a3, a4} whose matrix is given by 1 0 1 0 0 1 0 1 1 0 1…

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Q: If α and β are transformations on a set S, prove that α-1 ∘ β-1 and β-1 ∘ α-1 are transformations.…

A: Linear transformation are represented as the matrix . If A and B are two matrix then (AB)-1=B-1A-1…

Q: (R) → M2 (R) defined by adA (B) = AB − BA is a linear transformation. Find bases for the kernel and…

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Q: (b) Let B = {r, t, s} and R2 is a relation on set defined by the following matrix [1 1 1] 0 1 0 0 0…

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Q: a b = a² + b² (b) c d

A: (b) Given that, Tabcd=a2+b2 To find whether the given T is linear transformation. (i)…

Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: 1 Assume that Pr[A]=0.45 Pr[B]=0.65, and Pr[A∩B]=0.25  A. Pr[B Compliment ∩ A]= B. Pr[A Compliment…

A: Given, Pr[A]=0.45 Pr[B]=0.65 Pr[A∩B]=0.25

Q: b) Show that the function f(x) = x7 +1 is invertible %3D

A: Given that  f(x)=x^7+1

Q: (b) Let the function g : Z → Z be defined by g(x) = 7x + 3. (i) Show that g is one-to-one. (ii) Show…

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Q: Let T1and T2 be normal

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Q: Let f map C2 into C2 be a linear operator such that for every x in C2, f(f(x)) = x. Let V+ = {x in…

A: Let f:C2→C2 be a linear operator such that for every x∈C2, ffx=x.  Suppose V+=x∈C2:fx=x and…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.