Exercice 4: Show that the ring L = Q[X]/(3+3X +3X² +3X³ +3X¹ + X5) is a field. Compute the inverse of 1 + X² in L.

Q: f: {0,1} → {0,1}4 f(x) is obtained by removing the second bit from x and placing the bit at the end…

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Q: Find a basis for the eigenspace corresponding to the eigenvalue. 4 A = - 2 - 1 1 - 3 1 6 - 1 6 λ = 3…

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: 5. Find the kernels and images of the following homomorphisms. Which of the homomorphisms are…

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Q: 5. A child spins a hoop about her foot at an angular velocity of 4.1 radians per second. Determine…

A: Given that the angular velocity of the hoop is 4.1 radian per second and the diameter of the hoop is…

Q: ek 5. Let a = pt¹ …pºk, and b = pf¹ ...pf, where p; are prime numbers, and ei, fi ≥ 0. Show that…

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Q: Find all real solutions of the following rational equation and check any results. 5 X+6 1 + -=1 X

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Q: d) dª y dx4 +81y = 0

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Q: Let σpo := (<) be the usual signature for strict partial orders. A linear order (A, <) is called…

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Q: Solve the equation using the method of undetermined coefficients. a) c) d² y_2dy - 8y = 2e² dx² dx…

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Q: A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur…

A: For swimming, the sample mean and sample standard deviation were 187.0 and 7.2, respectively.…

Q: Let y = 2 8--8-8 աշ 5 Are ₁ and ₂ orthogonal? choose Compute the dot product between ₁ and ₂. U₁ •…

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Q: Supposer FCE, 9cE is algebraic F and dog (a/F) 13 odd. Prove that F(a)= F(a₁²). Hello 127 Over e Uso…

A: Using tower law as mentioned we solve this problem.

Q: The functions of interest in hydrogen atom theory are: 1+1 -2 21+1, f₁(x) = x¹+¹ e "L (+) n-1-1 In…

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Q: 2. Below is the definition of continuity, which you'll see in lecture soon or have already seen in…

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Q: (1) In (Z,+) determine ({2, 4,5}), the subgroup gener set {2, 4, 5). (As always, please provide full…

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Q: Given that p, = x² + xy, calculate fsp,ds over the region y ≤ x², 0<x< 1.

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Q: lem #1: Let v₁ = (2, 1, 0, -1). v₂ = (0, 1, 2, 1). and b = (1, 7, -1, −5). Let W be the subspace or…

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Q: 5. Is the given function even or odd or neither even nor odd? Find its Fourier series be if p = 1.…

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Q: Prove by Mathematical Induction that for all natural numbers n ≥ 5. Note: n! 1-2-3 (n-1). = n! >…

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Q: Find the first partial derivatives of the function. x³ - y6 fx = fy f(x, y) = +3 to x⁹ + y8

A: We have

Q: 4. (i) Write the following permutations in S9 as a product of disjoint cycles 6 1 2 3 4 5 6 7 8 9 7…

A: Note: As per our guidelines, we will solve first three sub-parts. Please repost remaining parts.

Q: Prove or disprove each of the following two statements. (i) For all integers x and y and natural…

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Q: What is the formula to create B-splines of different degrees? Can you use that formula to find…

A: B-spline basis functions of different degrees can be generated using the Cox-de Boor recursive…

Q: For each of the following sequences state whether or not it converges to zero, and prove your…

A: We use monotone convergence theorem to deduce that the sequence converges and then find the limit.

Q: For the matrix, list the real eigenvalues, repeated according to their multiplicities. The real…

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Q: It can be shown that the algebraic multiplicity of an eigenvalue λ is always greater than or equal…

A: We need to find the value of h so that the dimension of eigenspace for =3 is 2.If A is a matrix then…

Q: Find a basis {p(x),q(x)} for the vector space {f(x)∈p2[x]|f′(−3)=f(1)} where p2[x] is the vector…

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Q: Determine the following using the above diagram: a) What do the broken lines in the diagram above…

A: It is a set of multiple questions.Moreover, question number one has multiple sub-parts.As per the…

Q: Determine whether or not the following sets S of 2 x 2 matrices are linearly independent. Select an…

A: We Know that,  Linearly Independent &amp; Dependent : Two or more vectors are said to be linearly…

Q: Vi v₁ = 1. Let U span (G.D) be a subspace of R³. Answer the following questions based on this given…

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Q: 1. Show, using modular arithmetic, that for all n € N, 3(7³n) + 2n+³ is divisible by 11.

A: To show:  is divisible by 11 for all , using modular arithmetic

Q: A game involves drawing a card from a deck of cards. If you pick a 10, you get $0.50, if you draw a…

A: In a standard deck of cards, there are 52 cards.The game described involves drawing a card from this…

Q: The domain and target set for functions f and g is the set R. f(x) = |x| g(x) = -5x+2 Select the…

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Q: Two random variables X and Y with a joint PDF f(x,y) = Cx+y for 0≤ x ≤5 , 0≤ y ≤8 and constant C…

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Q: The product of 3371 and 1259 is 4244089. What is the gcd of 3371 and 4244089? 01 O 1259 0 3371…

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Q: If lim q →1 [ƒ(q) + 2²-119-12 lim[f(q) - 2q]. 9-1 = -4, use the Rules of Limits to evaluate

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Q: Four prizes are hidden under 20 blocks. One prize is worth $10,000, two are worth \$5,000, and the…

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Q: For the given cost function C(x) = 52900 + 200x + x² find: a) The cost at the production level 2000…

A: For the given cost function C(x) = 52900+ 200x + x2We are to find:a) The cost at the production…

Q: Find Hint: You may consider the following steps . Observe that and then show that • Show that •…

A: The given series is .The aim is to find the sum of the series using the sum of partial series.

Q: Y(s) = alue, yss. Remember 2s² +2s + 10 s(s² +68+5) to check the conditions of the FVT. Please

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Q: 10. Suppose (an}, {bn} are sequences of nonnegative real numbers with him bn = b = 0 and lim a, = a.…

A: 10. Given that are sequence of nonnegative real numbers with        and       To prove that:

Q: Consider the piecewise defined function Find the values of a and b that make the following function…

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Q: 3-6. Consider IR3 with the inmer product <xiy z:: = XT 2 10 12-1Y 0-1 2 Furthermore, we define 4₁,…

A: Given the inner product . Also,  be the standard basis in ?R3.(a)For a subspace U=span{e1,e3}, the…

Q: Show how to do part 3 please!

A: It is a linear regression problem with a best fit line. The main of that method is there are some…

Q: A loan of $1700 is being paid off by quarterly payments of $130. If interest is at the rate of 2%…

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Q: Use the characteristic root technique to find a closed-formula for the Fibonacci numbers. Your…

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Q: Let C be the circle given by x² + y² = 1. Evaluate √(-2x²y + cos x)dx + (2 xy² + y²e³)dy going in…

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Q: 2. Consider the function f(x) = x In(x). Now answer the following: (a) Evaluate the numerical…

A: note :As per the instructions we will only solve part (a), (b) of the question.As per the question…

Q: Solve the following differential equations a) y(x-y)dx + x²dy = 0

A: We have to solve the given differential equation. "Since you have posted multiple questions, we will…

Q: Which of the following subsets is a subspace of the vector space Fnxn of n x n matrices with…

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