Find the order of the given factor group (Z3 x Z6)/<(1,1)>

Q: Compute the factor group (Z6 x Z4)/(([2]6, [2]4))

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Q: When do you use a t-test for independent groups and what do the numerator and deniminator in the…

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Q: What are Bernstein polynomials?

A: A polynomial is basically a function, which can either be quadratic, cubic and so on in which the…

Q: Find all units and zero divisors in Z(18)

A: Sol:- The ring Z(18) consists of all residue classes modulo 18. In other words, Z(18) is the set {0,…

Q: Simulate the product algorithm for polynomials p and q where p( x ) = 2x³ - 3x² + 9x + 11 and q( x )…

A: Here two polynomials are given p(x) and q(x), we have to perform multiplication of the given…

Q: give the order of the element in the in the factor group (2,5) + in (Z3 x Z6)/

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Q: The number of subgroups of is 48 (A) 10 (B) 2 (C) 8 (D) 24

A: Given group is We have to find the number of subgroups of We know thatIf d is a positive divisor of…

Q: Let (a1a2a3a4) and (a5a6) be disjoint cycles in S10. Show that there isno element x in S10 such that…

A: Given: a1a2a3a4 and a5a6 are disjoint cycles in S10.We need to show that there is no element x in…

Q: Find the multiplicative inverse of 3 in GF(13) domain using Fermat’s Little theorem.

A: We have to find the multiplicative inverse of 3 in GF(13) domain using Fermat's Little Theorem.…

Q: Find the order of the given elements in the factor groups. (a) 7+ (3) in Z15/(3). (b) (3, 1) + ((1,…

A: a) we need to find the order of the element 7+&lt;3&gt; in ℤ15/&lt;3&gt; Since,…

Q: Define Group theory ?

A: To define group theory

Q: The group (Z4 ⨁ Z12)/&lt;(2, 2)&gt; is isomorphic to one of Z8, Z4 ⨁ Z2, orZ2 ⨁ Z2 ⨁ Z2. Determine…

A: Consider the group elements, Here the order of K is 6. Consider the order of group, The order of G…

Q: Consider the factor group G = R* /Q*. Determine which of the following elements in G are equal. 1Qx,…

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Q: Which of the following is a factor of P(x) = x3 - 3x2 - 3x +9 c) (x + 3) %3D a)(x - 3) b) (x – 2) d)…

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Q: What polynomial describes the graph below?

A: To find : The polynomial the given describes?

Q: If P, be a polynomial of degree n, i.e., P, = aok" + a;k"-1. + a, then A" P. = aon!.

A: We have to solve given problem:

Q: Determine the groups of order 45

A: By Sylow's theorems, the number of Sylow 3-subgroups must divide 45 and be congruent to 1 modulo 3,…

Q: 1. Consider the following data points (0,3), (1,0), (2, 1), (3,0) (a) Derive the monomial…

A: Given data point is (0, 3), (1, 0), (2, 1), (3, 0) Solution a: For 4 data point, monomial basis,…

Q: For groups Gı and G2, determine the center of G1 × G2.

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Q: Which of the following polynomials is an element in the span of the polynomials 1 + x + x³ and x+x²?…

A: Definition:

Q: How do i find the ral seros of  a given polynomial and their corresponding multiplicities?…

A: We have to find the zeroes and their multiplicities.

Q: (a). Show that the addition of x²+x and x²+x+1 is in GF(2³) (b).Show that the multiplication of x²+x…

A: We know that GF(2m) are the binary polynomials, i.e. polynomial whose coefficients are either 0 or…

Q: Find the index of in the group Z24

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Q: Q2: If G = R- {0} and a * b = 4ab ,show that (G,*) forms a commutative group? %3D

A: To show for the commutative group of (G, *), we verify the following properties of the commutative…

Q: express Z10 as a product of Z5 x Z2 , verify that both groups are isomorphic.

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Q: 2. Divide the following polynomials using long division, and indicate the quotient Q(z) and the…

A: We have to find

Q: In the characteristic polynomial (3 – A)(4 – A)³(–3- )(3 – 1), what is the multiplicity of d = -3?

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Q: In the group Z8 compute, (a) 6+7, and (b) 2-1.

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Q: Let G = Z4 x Z6. Compute the factor groups G/((2, 3)) and G/((3, 3)). (In each case, write the…

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Q: (c) How many of the elements of Z186 have multiplicative inverses?

A: To find the number of elements in the set of integers modulo 186, which have multiplicative inverse.

Q: What is the order of the group  ℤ10 x  ℤ15 x U(10) /〈(9, 10, 7)〉?

A: To determine the order of the group ℤ10 × ℤ15 × U(10) / 〈(9, 10, 7)〉, we need to divide the order of…

Q: In the group U (16) compute, (a) 5-7, and (b) 3-1

A: M(16) refers to th e multiplication group of non-negative integers (mod 16) that are less than 16…

Q: Find the decomposition of the representation Sym³V

A: The objective is to find the decomposition of the representation of Sym3V

Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 0.4 0.8 1.2 1.6 2 Ly 0 0.25 1…

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Q: Find the inverse of the element 9 in the group (U(10), ®10).

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Q: What is the order of the unique Lagrange inter- polating polynomial that passes through n + 1 data…

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Q: Q4) Fit a second order polynomial to the following data 5 6 1.2 1.6 4 6.25 i 1 3 4 0 0.4 | 0.8 0…

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Q: Find the LCM of the polynomials 1.x²³²-²³² and X²²=-2xy + y²2² 2 X HI 2.5x³y and 15x² Y

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Q: Find all the elements of a factor group Z3 X Z4 /

A: We have to find the all the elements of a factor group ℤ3×ℤ4/2,2 Let the group H=ℤ3×ℤ4 Then order of…

Q: If GCD of (a,b) is 1 we can find the lcm by multiplying a and b. True or false

A: if GCD(a,b) is 1, We can find lcm by multiplying a and b.   This statement is True.

Q: Why use f test when there are 4 groups? I would appreciate it if you could explain in detail.

A: Why use F test when there are 4 groups?  Concept Used: Independent t test is used for comparing one…

Q: Q// Fit a second-order polynomial to the :following data Y 7 11 7 5 2 10 4 7 2 11 11 3 y = 8.440138…

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Q: Show thet tegular a S(G) = A(G). G

A: Let us assume that graph G is regular. Now,  δ(G)= degree of the vertex with minimum degree…