compute the following in Z12: [9]+[11], [5]-[8], and [7][9].

Q: Show that MnXn and Rn^2 are isomorphic.

A:

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'…

A:

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

A:

Q: Show that under the transformation: k= the equally spaced z-values, z : 1o, To +h, xo +2h, .…

A: Just substitute the given values of x and proof will follow.

Q: Find the coefficient of x²y² in the expansion of (–x+ 3y)*.

A:

Q: Exercise 5.4.18. Give a similar proof that 1 is the multiplicative identity for Zn when n > 1. What…

A: To show 1 is the multiplicative identity of  ℤn for n>1 and 0 is the multiplicative identity of…

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A: A manufacturing company employs two devices to inspect output for quality control purposes.

Q: In Z3×U3, Find the order of (1, 2). Show your work.

A:

Q: Which of the following elements in Z8000000 is not of order 8? 7 000 000, 2 000 000, 3 000 000, 5…

A:

Q: (b) 1 = -4 - 4- 2.

A: Given that

Q: Find the order of the residue class 5 in Z/29Z.

A:

Q: This exercise provides an alternative to Theorem 8.2 for factoring an r-cycle into transpositions.…

A:

Q: Suppose that b₁ = 2bn-1 +15bn-2 for n ≥ 2, with b = 5 and b₁ = 1. Solve this recursion to obtain a…

A:

Q: Prove that coth-la = In x +1 for |a| > 1 x - 1

A:

Q: In Z[i], show that 3 is irreducible but 2 and 5 are not

A:

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

A: Using Z transform

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

A:

Q: Which term of the expansion of (z + 4) contains z Term number contains z4.

A: Given expression is: (x4+4)16

Q: Compute |A| for the following:

A: We have to compute A for the following given matrix: A=210121012 We know to determine the…

Q: Prove that x4 + 15x3 + 7 is irreducible over Q

A:

Q: Given that the points (4, 5), (5, 6), and (6,8) function f, find f1(6). points on the graph of an…

A: Given that f is invertible Function ⇒f and f-1 are one to one and onto

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

A:

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

A:

Q: Find ²2 of z = In(xy) 8²y

A: Given: z=lnxy   As we know that; The Power law; ddxxn=nxn-1 The Chain Rule: fgx'=f'gx·g'x And…

Q: Find all the generators of Z24-

A:

Q: There are two different formula or methods that can be used to See. A- under what circumstances is…

A:

Q: Show that 2Z ∪ 3Z is not a subring of Z.

A: Theorem for Sebring Test: For any ring R, a subset S of R is a subring if and only if: it is closed…

Q: Find the ordinary generating function for the number of partitions of n in which no part occurs more…

A:

Q: Find all the generators of a) Z10 b) G = , where G'has order 30. %3D

A:

Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

Q: Find the splitting field of x4 + 1 over Q.

A:

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A: Given: For X Number of trials (n1) = 4 Probability of success (p1) = 0.993 For Y Number of trials…

Q: Show that Z4 is not isomorphic to U(12) by comparing the orders of elements.

A: z4=0,1,2,3 is group w.r to +order of elementsoa=n⇒an=e where n is least positive…

Q: Demonstrate that x' + 3x – 8 is irreducible over Q. -

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: Show that 1 is the only solution of x25 - 1 = 0 in Z37.

A:

Q: How many elements of order 4 does Z4 ⊕ Z4 have? (Do not do this by examining each element.) Explain…

A:

Q: Find all subfield of Z14

A: Z14 is not a  field reas is given on the next step.

Q: The characteristic of Z5[x]/ is

A: Introduction: Suppose, Rx be a ring of polynomials and Px be any polynomial. If there exists an…

Q: {3* + (-3)k + 3k}

A:

Q: How many integer elementary decompositions does the number 30 have?

A: Let pn denotes the number of partition of an integer in to elementary decomposition. That is, pn…

Q: 4. From the field of (Z5, , (mod 5)), obtain two MOLS of order 5.

A: When p is a prime number, the field ℤp is the set ℤp=0,1,2,3,....,p-1. Over the elements of ℤp, a…

Q: 4. Prove that x – 15x³ + 10x² – 21x + 2021 is irreducible in Q[x]. -

A: Given :-  Prove that x5 -15x3 +10x2 -21x +2021 is irreducible in ℚx.

Q: even and n > 4, show that rk is an element of order 2 which commutes with all elements of D2n

A: Given, n = 2k is even and n ≥ 4, We have to show that rk is an element of order 2 which commutes…

Q: How can I find all monic divisors of degree 1 in Z_7 [x], 5x^2+5x+4? please help me get started with…

A: Set of all Polynomials over a field ℤ7 is given by ℤ7x=anxn+an-1xn-1+ . . . +a1x+a0  where a0,a1, .…

Q: 5. Compute for the product of the complex coardinates :(3, 1)(3, - 1) a. (2,1) b. (1,1) c. (3,1) d.…

A: The given problem is to find the product of the given complex coordinates, We have to use product of…

Q: Which is the expandison of x2-y2

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

Q: 1. Find the first-order derives:

A: Given,      4x2+715x4+534x3-37x6+15x-30

Q: In Z[V-5], the element 29 is: None of the choices Irreducible Unit reducible

A: