If a and bare nilpotent elements of a commutative ring, show that a + b is also nilpotent. Give an example to show that this may fail if the ring is not commutative.

Q: Consider the matrix equation -12 4 0 4 000 16 -9 00 16 -9 4 0 -9 16 4 04 00 00 1. Using LU…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Let At be a matrix that depends on r and is given by 4-[30] At = t (a) For which te R matrix At has…

A: At=-13t-21

Q: Jo (x) = -—- f* T cos(xcos 0) do = 1 -=-65² JO cos(xsin 0) de

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Q: Evaluate (x+y-52) dV where E = {(x, y, z) | − 7≤ y ≤0,0≤x≤y, 0≤ z ≤ x + y²}

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Q: 4. Write y as the sum of two orthogonal vectors, y, in L and y₁ in L Let y = YL = 1 and u = 2 7 Let…

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Q: u v If (x + iy)³ = u + iv, then show that + = (x² - y²). - X y ---

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Q: Calculate the requaested distance. 1. The distance from the point S(7, -2, -5) to the plane 2x + 2y…

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Q: (3) Determine the number of terms in series of ln(1+z) needed for computing In 1.1 with error less…

A: A Taylor expansion of ln(1+x) is given. One has to determine the number of terms in the series of…

Q: A steel ball weighing 1lb is dropped from 2500 ft. with no velocity. As it falls, air resistance is…

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Q: 3. Numerical Methods. Using Improved Euler method, solve for yı if x₁ =1.0: y = ² + e-x² y(0) = 0.2…

A: Given Data: Let us consider the given data, y'=y2+e-x2y0=0.2n=0x1=1

Q: Complete the following table. Population Growth Rate, k Doubling Time, T 2.7% per year Country A…

A: A=Pert where P =starting population at time t=0, t=years, r= interest rate ( in decimal) e =about…

Q: Let g(x, y) = −4 - x3 + x2 - 6 - y2 - 3. a. b. дд дх ав a дд ду ав sin (a) sin (a) Show/hide Ә Ox f…

A: gx,y=-4x3+x2-6y2-3

Q: Determine whether the polar conics below are circles, ellipses, parabolas or hyperbolas. What is the…

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Q: 2 Find the length of the curve y = 3/2 from x = 0 to x = 4.

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Q: Using the given graph, approximate the area under the curve from x = 3 to x = 6 using 3 subdivisions…

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Q: Prove the following result: the curve y(x) that extremises the functional 1 - 1/² √² + (0²) ² dr =…

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Q: techniques we have been learning. s(t) 7.00 t 0.00 Answer the following based on the table of the…

A: As per the question we are given the following data table about the position s(t) and time t s(t)…

Q: Find the area between the two curves 2 1+2x²¹ Sketch the region in question. y = y = 2x² - 1

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Q: Consider the following theorem. Theorem If f is integrable on [a, b], then n f(x) dx = limf(x)Ax i =…

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Q: (b) y" +9y = sin 2x, y(0) = 1, y'(0) = 0

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Q: Identify one point at which the gradient of the function is 5i + 5j. (x, y) f(x, y) = = -8x² - 7y² +…

A: The gradient of the function

Q: Determine if the set {x + y∛2 : x,y ∈ Z} is a ring. If so, please prove why. (Z represents integers)

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Q: 54 people are competing in an athletic event. The top 4 competitors receive prize money, with 1st…

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Q: A cost function is given. C(q) = 3900 + 6q-0.01q2 + 0.0003q³ (a) Find the average cost and marginal…

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Q: Given the vector field F = (e',e¹) and the curve C going from point A to point B shown in the…

A: The given vector field is F=ey,ex. The curve with vector field is given. To Check: whether the given…

Q: Problem 3. (a) e (c) Let A be an n x n matrix with characteristic polynomial: f(t) = (-1)" t" +…

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Q: w is an imaginary root of unity. Prove that 3 (i) (a+ba+ca)³ + (a+ba² + ca)³ = (2a-b-c) (2b-a-c)…

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Q: May i please request a hand written solution

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Q: Let 2₁, 22, 23 be three complex numbers and a, b, c be real numbers not all zero, such that a+b+c=0…

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Q: Introduction to Discrete Mathematics Let (un)n∈N be the sequence defined by recurrence as follows:…

A: u0=5 un+1=3-2un

Q: Suppose you plan to have $30,000 in 10 years from now and you can invest your savings at 2%…

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Q: Can we make the matrix J = B₁ = B₂ = B3 = B4 = 02 [12] Answer: J = -1 0 - 2 [²2¹] 3 8 5 1 1 36 Yes,…

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Q: • Matrix N € Cnxn is said to be nilpotent whenever Nk = Onxn for some positive integer k. • The…

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Q: Solve for z: 2²-(3-2i)z =(5-5).

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Q: a носо many paths are there from A to B along vertical and horizontal lines in which you are only…

A: Solution of the question is given below.

Q: Mary Branson invested her summer earnings of $3000 in a savings account for college. The account…

A: Given   Principal amount = $3000  Interest rate r = 3.5%  Time t  = 6 months  We need to find amount…

Q: Is f(x) = x / (1+sqrt(x)) uniformly continuous on [0,1] and [0, infinity).

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Q: Z₁ Z₂ are two points in an Argand plane. If a Z₁ = b|Z₂l, ther # prove that az₁-bZ₂ aZ₁ +bZ₂ is…

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Q: Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be…

A: As per the question we are given the covariance matrix of a students' data and the index : y = c1x1…

Q: Numerical Methods. Using h = 0.2, approximate the value of y (3) for the given differential equation…

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Q: 16 D 13 18 27 10 a 10 24 B 11 E 20 2 Find the shortest path from vertex A to vertex B. Give your…

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Q: Let Q[√c] denote the set of numbers a + b ⋅√c, where a,b ∈ Q for some c ∈ Z. I must prove that Q[√c]…

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Q: Using the inner product (, ): M2×2 × M2×2 → R, (M, N) = (MNT)₁,1 + (MNT) 2,2 calculate -2 3 1 -…

A: Given: .:M2×2×M2×2→ℝ, M, N=MNT2,2+MNT2,2 To calculate: -2347, -1-344.

Q: 3. Suppose that p is a nonzero continuous operator such that p is Hermitian (i.e. p* = p). (a) Show…

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Q: Let F(x, y, z) = (y² cos z, 2xy cos z, – xy² sin z) and C₁ : R(t) = (t², sint, t), t = [0, Evaluate…

A: The given vector function is, F(x,y,z)=y2cosz,2xycosz,-xy2sinz, the curve is: C1: R(t)=t2,sint,t,…

Q: Find all the solutions to z7 = 1 - i√3, and plot them on the complex plane. Show that (cos 0 + i…

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Q: 3) Is f(x) = (x) / (1+sqrt(x)) uniformly continuous on [0,1] and [0, infinity).

A: The given function is, f(x)=x1+x. To Check: whether f is uniformly continuous on [0,1], and [0,∞).…

Q: (4) Use the complete Horner's algorithm to write the Taylor series for the following function at the…

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Q: Suppose you have a vector field F(x,y,z), as defined in the provided image. Find the work that is…

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Q: Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on…

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