What is the kernel of homomorphism of \phi:Z4->Z10 defined by \phi(x)=5x?

Q: Verify that the Galois imaginary is primitive in GF(3, x³ + 2x+1)

A: Given:- Verify that the Galois imaginary is primitive in GF(3,x3+2x+1)

Q: b. In Z6(x], let f = 2 + x + 4x² + 3x³ and g = 4 + 3x+ 5x² + 3x³. Compute f + g and f.g and their…

A: In the finite field we only use the coefficients from that field . The degree of polynomial is not…

Q: How many invertible functions exist with the signature Za→ Zb if a = b? %3D

A: To find the number of invertible functions from ℤa to ℤb. Given that a=b. Also ℤa has a elements.…

Q: * find z- transform for -4 x (n) = { 2 1 2 3} x(2) = 2 +z + 2z-2 + 3z-3 x(2) = 222 + z +=+ 2 + 3Z'…

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Q: Find a basis for span(l - 2x, 2x - x2, 1 - x2, 1 + x2) in P 2.

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Q: to find the z-transforms of following: {ak-3} (3k-4)

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Q: find the generated of zy zs+Z7

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Q: Prove |°z 'z|>|°z|-|'z|

A: We have to prove  z1-z2≤z1-z2            orz1-z2≥z1-z2 NOTE : The polar form of a complex number…

Q: Without looking at inner automorphisms of Dn, determine the numberof such automorphisms

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Q: Prove that the mapping from R under addition to SL(2,R) that takes x to  [ cos x     sin x  -sin x…

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Q: Find the Fourier expansion of f (x)=-x; – x<xST;

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Q: Show that the mapping a → log10a is an isomorphism from R+ undermultiplication to R under addition.

A: To show: The mapping a → log10a is an isomorphism from R+ under multiplication to R under addition.

Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

A: In this question, the nested algorithm to convert the polynomial 1+2x+3x2 into its equivalent Newton…

Q: 3. Solve for the Z-Transforms and ROCs of: x[n] = [6, -2,2,0,0,4, -3]

A: We have to solve the given problem.

Q: Determine the minimal polynomial of 2/3 – V5 ov over 0.

A: That's easy. Have a great day!!!

Q: Find all possible homomorphisms form Z10 → Z4. Then find the kernel of each of these homomorphisms.

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Q: Find the wronskian of f1=x4, f2=-x4, f3=x2, f4=-x2

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Q: The z-transform of Z{3k} O 1/(z-1)^2 O 3z/(z-1)^2 3z/(z-3)^2 3z/(z-1) z/(z-1)^2 O z/(z-1) O…

A: This question is related to Z transform,  we will solve it using given information.

Q: The z-transform of [n] = u[-n] is

A: Using Z transform

Q: What is the impact of the first isomorphism theorem??

A: Impact of first isomorphism is a isomorphism between quotient of group and normal group is…

Q: Prove Theorem 11.3

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Q: If (a] € Z/mZ is invertible, is [-a] invertible? If yes, prove it and say what the multiplicative…

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Q: Orthonormalize the set {(¿).(9)} with respect to the inner product from before.

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Q: Find the order of [5] in Z23 using Fermat's Theorem.

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Q: Find Z-transform and ROC f x(n) = {1,2,−1,2,−1}

A: Given that: xn=1,2,-1,2,-1 The objective is to determine Z-transform and ROC. Let consider,…

Q: Show that (an) is increasing

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Q: Provide a two-column proof of Theorem 3: Finite Subgroup Test.

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Q: Prove that K4 is not outerplanar

A: In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices…

Q: Write all essential submodule of Z 24 as Z-module.

A: (C) We know that a submodule E of M is essential if it has a non trivial intersection with every non…

Q: prove that esch'x - In (* + x2 %3D

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Q: Determine the z transforms of the sequences (a) {(-} (b)

A: Use the formulas below to obtain the Z-transform.

Q: What is a mapping of phi defined by the automorphism of Z6?

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Q: Determine the galois group

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Q: p be an irreducible reprsentation of G

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Q: Compute the indicated values for the indicated homomorphisms.…

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Q: Use Eisenstein Criterion to verify that , If p = 2, f(x) = x² – 2 is irreducible %3D over Q. State…

A: Explanation of the solution is given below...

Q: Find the Z-Transform for x(n) shown below including the ROC * 4

A: We know that the z transform of the sin function is given by sin z=z-z33!+z55!-... Using this we can…

Q: b) Let 0: Zg – Z4 given by Ø(x) = 2x Show Ø is homomorphism %3D Determine the kernel of Ø Determine…

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Q: 8. Describe all homomorphisms from Z5 into Z, and compute their respective kernels.

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Q: 7. Use the binomlal theorem to expand (x+x-1] and simplify the result. Show your work.

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Q: 3 use the definition of latlace transforms to find £{+²H (E-5) } JINO

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Q: (1) Show that there are infinitely many irreducible polynomials in F[].

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Q: How do you interprete the main theorem of Galois Thoery in terms of subgroup and subfield diagrams?

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Q: Which is the expandison of x2-y2

A: Given data:- The given equation, (x2-y2)

Q: Prove that le-2z| 0.

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Q: Exercise 3.2.3 Show that Zg under addition is isomorphic to Z; under multiplication.

A: We know that Z6 = {0, 1, 2, 3, 4, 5} and Z7* = {1, 2, 3, 4, 5, 6}. A group isomorphism is a function…

Q: Determine the z transforms of the sequences (a) {(-}}'} (b)

A: Z-transform: The Z-transform of a sequence is given by, Given:  a)  b)