FIND the splitting field E of x⁵− 3 over Q and [E : Q]. Justify your answer completely.

Q: Prove that Z[i]/ is a field.

A: First Let us observe that 1+<1-i>= -1+<1-i>

Q: Find the z tronsfom of f(n) = a" cos (bn).

A: We have to find the z transform of the following.

Q: 4. Find the inverse z- transform of the following 3 de XCZ)= tanh (z-)

A: Given: Let us find the inverse z-transform of the given following, xz=tanh-1z2-14

Q: If F is a field then F[x,y] is not a P.I.D

A:

Q: Prove by mathematical induction that, for all positive integers n, de (e* sin x) = 23"e* sin(x…

A: To Prove →dndxn ex sin x = 212n ex sinx + 14nλBy mathematical induction for all positive integen…

Q: What is the inverse transform of F(s) = In (s'/Vs2 +4s +5}

A:

Q: Zg /2Z, is a field Select one: O True O False

A:

Q: 2 Determine the inverse transforms of the following. 2s² – 6s – 1 (d) (s – 3)(s² – 2 + 5)* Exercise

A:

Q: Consider the set S = 2n 1 :m, n EZ} equipped with the usual addition and multiplication. (a) Does S…

A: As per our guidelines we can answer only 3 subparts of a question. So kindly repost the remaining…

Q: Give the Laplace transform of 4x+4 0<x and x < 2 f(x) = -3 2 3x 3 1 + -2s +e 10 3 a) O F(s) = - 5 2…

A:

Q: Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

A: Given, fx=cosax,x≥00,x&lt;0 As we know that, Ze-ax=1+e-aτ+e-2τz-2+...=11-e-aτz-1=zz-e-aτ

Q: 25. Suppose 2 = {e'2T,0 < 0 < 1} is the unit circle. Let A be the collection of arcs on the unit…

A: We are given the set,  Ω={ei 2πθ, 0≤θ&lt;1}. which is a unit circle. Also, we are given a collection…

Q: omot rix over the field F& roo- Every equitha lemt to mx n veduced metoix.

A: Given a m×n matrix.

Q: Let K = Q(i) denote the field of Gaussian numbers. Note that 10 = (3 + i)(3 − i) = 2 · 5. Is this…

A: Answer is yes. To aprove i have used the definition of UFD

Q: 36 MO - * (1 The direct sum of the field (Q,+;) with itself (Q x Q.0.0) is a) Field b) Integral…

A: The direct sum of yhe field with itself is an integral domain So right option is option b) integral…

Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

A:

Q: Problem 3.6. Find all irreducible elements of Z[X], k[X,Y]. Prove that they are also prime elements.…

A: To find the irreducible elements in Zx, first  we have to find the unit elements in ZxDefinition of…

Q: Solve the following problem given that the scalar field f = xy? + 3xiz². Find Vf at point (8,1 -2).…

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Q: what is the Fourier transfrom of the following 0.5 d²x(t) j2nf dt2

A: In this question, the concept of Fourier Transform is applied. Fourier Transform The Fourier…

Q: The Fourier transform of x(t) = 9+4t2 IS 37|f "e 3m1F] 2 77 O X(f) = 7T OX(f) = 27|f 2 37 OX(F) = -…

A:

Q: Q2: Find the inverse Z transform of the following: 2. X (z) = (a)/z %3D 2-1

A: When we transform a real-time signal into the complex plane, we follow the Z-transformation. In a…

Q: Q2: Find the inverse Z transform of the following: 1/z 3. X(2) = z-1

A:

Q: Consider the function S e20x+2, if x 0 The Fourier transform of f, defined by F(f)(§) := f…

A: Integral 0 to infinity the function must be zero. So only - infinity to 0, the integral exist.

Q: (b) What is the Fourier Transform of x?8(x² – a²)?

A: The given problem is to find the Fourier transform of the given function, in the given function…

Q: 2. Consider the field F = (2x – 3y)i + (-3x + 4y – 8)j + 0 k. (a) Determine whether this field is…

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Q: Prove the following combinatorial identities (algebraically): (") = Eo ("*) 1) ("") = E, () (") 2)

A: We have to prove thatm+n+1n=∑k=0nm+knProof⇒ As L.H.S is number of subsets {1,....,n+m+1} of size n…

Q: Obtain the Z transform of 10 s(s² +s+2)

A: We are given the Laplace transform fs=10ss2+s+2=51s-s+1s2+s+2=51s-s+12s+122+722-12s+122+722 So,…

Q: Consider the field Z3[x]/. Please explain to me how this field has 9 elements. Thank you!

A: Consider the field Z3[x]/&lt;x2 +x+2&gt;. Please explain to me how this field has 9 elements.

Q: 3. Suppose F is a splitting field of æ" – 1 over Z3. (a) Find |F| if n = 3. (b) Find |F| ifn = 13.…

A: Given polynomial is  Let p(x)=x^n - 1

Q: If R is a U.F.D., then R[x, y] is a U.F.D. If F is a field, then F [x, y] is à U.F.D.

A:

Q: Find the Z-Transform of x(k) = k? u(k) O a. 2z/ (z - 1)3 O b. 22/ (z - 1)? Oc. Oc. 22/ (z- 1)3 O d.…

A: Z transform

Q: Obtain the z-transform of the following: x(n)=na" sin(an)u(n)

A: Let us start solving the problem step by step.... We need to find the z-transform of x(n)

Q: 18. Is Q[x]/(x² – 5x + 6) a field? Why? 10

A:

Q: The element (3x-6) is Reducible over QO lucible over Q and R c. Both d. Other O O O O

A: The elements (3x-6) is_____

Q: If R is a U.F.D., then R [x, y] is a U.F.D. If F is a field, then F[x, y] is a U.F.D.

A:

Q: Q2: Find the inverse Z transform of the following: 1/z 3. X(2) = %3D z-1

A:

Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: (c) Let P = (2 : 5: 1) and Q = (9 : 6: 1) be points on the elliptic curve y? = x +7x +3 defined over…

A: Given: P=2:5:1 and Q=9:6:1 are points on the elliptic curve y2=x3+7x+3 defined over the finite field…

Q: Q2: Find the inverse Z transform of the following: 1/z 3. X(2) = 8-Z-Z Z-1

A:

Q: Check that this pattern is consistent with your substitutions, but you do not need to formally prove…

A: Given: Assume that, T1=1. (i) Assume that the recurrence relation isTn=Tn-1+1. Obtain the recurrence…

Q: 2. Compute the Fourier Transform of f(x) = e¬ax²

A:

Q: OR Find the complex Fourier transform of the convolution of f(x)= [3, -1<x<1 0, elsewhere, g(x)= X,…

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Q: Solve the following problem given that the scalar field f = xy? + 3x3z?. Find Vf at point (8,1, -2).…

A: Given function is, f=xy2+3x23z2  Now, calculating ∇f…

Q: Q2:(2/Ptiti.) is a Prime field; Pprime ? a.

A: The given problem is related with prime field. Given that,                 ℤpℤ , + , . , where p is…

Q: 3. Determine the Fourier transform of the following: f(t) = {el³6 0, -1 < t < 1 elsewhere

A: Fourier transform of f(t) F(f(t))=∫-∞∞f(t).ejstdt given function f(t)=ej3t-1&lt;t&lt;10elsewhere

Q: Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).

A: To prove dw=πδw-k+δw+k is the fourier series of cos(kt)

Q: Find the inverse transform 1 a[n] pX(2)z-1dz 2ni

A:

Q: If R is a U.F.D., then R[x, y] is a U.F.D. If F is a field, then F [x, y] is a U.F.D.

A:

Q: Find the Fourier-Hermite expansion of f(x) = x³, x E R.

A:

Q: Given the multiplication axioms of fields, where x ≠ 0, prove: a) if xy=xz, then y =z b) if xy=1,…

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