(1) Let h(x)=1+x²+x³+x* be the parity check polynomial of a C(7, 4) cyclic code. Find the corresponding message polynomial u(x).

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…

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Q: Write a polynomlal f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

A: Since x=-4 is a zeros so, (x+4) is a factor of f(x) Since x=1 is a zero so, (x-1) is a factor of…

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A: A set S  is said to be countable if it has a one - to - one function as f:S→N.

Q: 11. Write a polynomial to express the total value, T(x), of (x + 3) 20-peso bills, (x - 2) 50-peso…

A: Note:  We'll answer the first question. Since the exact question isn't mentioned. Please re-submit…

Q: Find the QR decomposition and prove -3 -5.

A:

Q: Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a monic…

A: Given: The zeros of the polynomial 3-i ,  i   and 2

Q: An operator whose minimal polynomial is different from its characteristic polynomial

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

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Q: (List all irreducible polynomials of degree < 2 in Z3 [x].

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

A: Given that

Q: The number of polynomials of degree 3 in Z5[x] is: O (4^4)*5 O 5^4 O 4^4 O 4*(5^3)

A:

Q: Find a monic polynomial f(x) of least degree over C that has the given numbers as zeros, and a monic…

A: Given, Zeros, -3i,4 it has three zeros ±3i, 4 these zeros are factor of the equation…

Q: Questron Sec 5.3. %4 ( Lincar Algebra) in I ) Find the least square gystann : solutren to the gotenm…

A: We need to find the least square solution of the given system of linear equations. We have…

Q: Let T(x1,x2)=(2x1-2x2,9x1-8x2). SHow that T is invertible, and find a formula for T^-1(x

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Q: Copy of In the characteristic polynomial (3 – A)(4 – 1)³(– 3 – AX3 – A), what is the multiplicity of…

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Q: Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced…

A: In the question it is asked to construct interpolating polynomial using the table given in question.

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: Determine the linear interpolating polynomial that passes through the points (2,4) and (5,1). p(x) =…

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Q: Use Cramer's rule to compute the solution of the system. 12x1 + 2x2 + 4X3 = 6 4X1 + 4x3 = 4 5x, +…

A: The given equation are: 12x1+2x2+4x3=64x1+4x3=45x1+3x2=2

Q: Describe the group of the polynomial (x4 – 5x2 + 6) ∊ ℚ[x] over ℚ.

A: Please see the next step for solution

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

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

Q: The number of reducible monic polynomials of degree 2 over Zz is

A: The number of reducible monic polynomials of degree 2 over Z3 is

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

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Q: Find the minimal polynomial for  ∛2 + ∛4  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: EXERCISE 5.4 Factorize each of the following cubic polynomials by factor theorem. 2 x --22x + 40 5.…

A: 8. Cubic Polynomial: 2x3+x2-2x-1 Take x2 common from the first two terms of the given polynomials.…

Q: (1) Let h (x)= 1+x²+x³+x* be the parity check polynomial of a C(7, 4) cyclic code. (a) Show that…

A: Consider the equation hx=1+x2+x3+x4 and C7,4. vx=x+x4+x5+x6

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

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Q: Employ Crout's decomposition to solve the system. 5x1 – x2 = 9 -x1 + 5x2 – x3 = 4 -x2 + 5x3 = -6

A:

Q: 4. Find the domain and codomain of the transformation de fined by the equations. Wi = 2x1 + 7x2 –…

A: Given: Let us determine the given domain and codomain of the transformation defined by…

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

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Q: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

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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: 2. Identify the approximate input values of any relative maximums and minimums of this 5th degree…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find the orders of all the elements of Ag.

A: A8 is the group of all even permutation of S8.

Q: 2. List all the polynomials in Z3[x] that have degree 2.

A: To find all the polynomials in Z3[x] that have degree 2

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A:

Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of 1- 1?

A: Ix=2x-18 Now let, y=2x-18 Now to find inverse function interchange x and y, then solve for y in…

Q: (1) Let h(x)=1+x²+x³+x* be the parity check polynomial of a C(7, 4) cyclic code. (a) Show that…

A: Given the code is a C7,4 cyclic code. Thus, the highest order of the code word will be k-1=4-1=3.…

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

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Q: Given two polynomials in from of x^3+x^2+x+c =0 x^3+x^2+x+c =0

A: Given: To find their intersection using matrices. Given two polynomials in from of…

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: 2-Suppose that you have n data points (x1, y1), ..., (xn, yn), with the xi all distinct. Which of…

A: Question 2 is related to Existence and Uniqueness of interpolating polynomials Question 3 is asking…

Q: Let A = k 0 1 k - 1 2k k+ 1. Use cofactor expansion to determine which values of k make A…

A:

Q: (1) Let h (x)=1+x?+x³ +xª be the parity check polynomial of a C(7, 4) cyclic code. polynomtak (b)…

A: The code is a C7,4 cyclic code. The parity check polynomial is  hx=1+x2+x3+x4. Now, the value of…

Q: -4 -11 25 16. Without formally showing that there is a nontrivial linear combination of x-2x, x++x³…

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Q: Find the minimal polynomial satisfied by √2 + √5. over Q.

A: We have to find the minimal polynomial which satisfied by 2+5 over Q.

Q: Find all the BFS of the linear program Мaximize 4x1 + 5^2 + X3 + X4 Subject to 2x1 – x2 + 3x3 + 2x4…

A: We know that if there are m equations in n unknowns then there can be at the most nCm BFS. As there…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.