Factor x4 1 completely in R[x] and then factor it completely in

Q: mistake

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Q: Show that each of the following are not inner products on R³,

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A: Here we have to find the matrix A, B and C.

Q: f 02 3 mere dz zi #-[21]) Z + N N 2 e*3% and Z=

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Q: The transformation x=u² + v- 1 takes the rectangle 0 ≤ u≤ 2 and 0 ≤ v ≤ 1 in the uv-plane to the…

A: Given: The transformation  and  takes the rectangle  and  in the uv-plane to the stranglely shaped…

Q: Find the dimensions of the following linear spaces. (a) The real linear space C7 (b) P₂ (c) The…

A: We have to find the dimensions of each of the following linear spaces.a) The real linear space b) c)…

Q: Suppose that V is finite dimensional real vector space and that ⟨⋅, ⋅⟩ is an inner product on V.…

A: Given V is a finite dimensional vector space over , say n dimensional, and is an inner product on…

Q: 10. Consider the following two 3 x 3 matrices -1 3 3 -2 -1 -2-2 1 (a) (6 AB (b) ( A = and 2 B = s)…

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Q: 8) Prove that 2 is a primitive root modulo 53.

A: We have to Prove that 2 is a primitive root modulo 53.

Q: Which of the following transformations are linear? Select all of the linear transformations. There…

A: Given statements are written as follows.(A)  from  to .(B)  from  to .(C)  from  to .(D)  from  to ,…

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Q: Math 151 - Workshop 13 (Riemann sums) We turn now to the problem of finding area under a curve.…

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

Q: 15= 1.2732M 2 + V 1.2732M 2 2 + (7.639)²

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Q: 2. Suppose that a and b are primitive root modulo an odd prime p. Show that ab is not a primitive…

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Q: 7) A student is enrolled in four courses that require submission of projects covering different…

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Q: (b) How many ways can the letters of the word MAILBOX be arranged in a row if M and A must remain…

A: We use techniques of basic counting to solve this question.

Q: If A = then det(A) Thus, -7 -91 3 A-1 -102 and det(A1) O is Nonzero 3 -34 34 [图] 3 7 -34 -102 x

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Q: Let f: R → R³ be defined by f(x) = (8x, –7x, –9x). Is ƒ a linear transformation? f(x + y) = f(x) +…

A: Let  be defined by .We know that a transformation  is a linear transformation, if  and  for all…

Q: (a) Let G be a simple graph with n vertices and m edges where m ≥ (^₂¹) + 2. (i) Let vand w be any…

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Q: Problem #3: Let A = 10 -1 0 0 -1 0 0 10 0 0 0 10 -1 0 -1 10 (a) Find the characteristic polynomial…

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Q: Find the corresponding linear system near each critical point.

A: For the non-linear system(c) To find the linear system corresponding to the equilibrium points.Here,…

Q: can you do part b please.

A: Proof: The statement is not necessarily true, and I can provide a counterexample to prove this.A…

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Q: 30. All Smiles Dental Clinic would like to develop a hygienist master schedule for the treatment of…

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Q: Find the general Solution For D-E y + y tan x = [cos²x] y¹ प्रे

A: Given, differential equationMultiplying above equation by y on both sides, thenFrom equation (ii)

Q: Find (with proof) the infimums of the sets S = {1 /n:

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Q: x f(x) 0 0 100 200 400 600 800 1000 0.82436 1 0.73576 0.40601 0.19915 0.09158 Find the value of the…

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Q: 14. In this question we will consider the surface S parametrized as r(u, v) = (u²+ v, u, v), (a)…

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Q: Determine the accumulated value after 14 years of deposits of $230.00 made at the beginning of every…

A: Given:There is 14 years of deposits of $230.00 made at the beginning of every year and earning…

Q: Part (a) Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = x/2. Use four…

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Q: If fis integrable on [a, b], the following equation is correct. f(x) dx = limf (r.) Ar, where Ar=!…

A: Consider definite integral .To illustrate the value for integral.If  is integrable on  then .Here…

Q: Quadratic Interpolation • a strategy for improving the estimate by introducing some curvature into…

A: Given information:x01002004006008001000f(x)00.8243610.735760.406010.199150.09158To find:The value of…

Q: 3. Find the interval of convergence of the series ☎ n=1 (-1)"+¹(x-2)" 3"-n

A: Find the interval of convergence of the series

Q: 1. Find the maximum and minimum values of f(x, y) = x² + 3y + 7 on the set R, where R is the region…

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Q: Find the radius of convergence, R, of the series. R = 00 I = W n = 1 7n n! Find the interval, I, of…

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Q: Problem 0.3 diverge: (4) Σ^=1 In(n) n 3 (5) En-2 (n²-1) Determine whether the following series…

A: Integral Test:  The integral test states that if f(x) is positive, continuous, and decreasing on the…

Q: 0 0 Which of the following transformations are linear? Select all of the linear transformations.…

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Q: 4. Let X be a metric space. Show that if every continuous function f : X → Ris bounded, then X is…

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Q: 1. First we focus on the sequence of squared Fibonacci numbers. Theorem 1 (Sequence of Squared…

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Q: Consider the graph G with the adjacency matrix: 0 G is a tree. G is planar. ✔G is connected. 0 G has…

A: Let  is a vertex set of graph.Then using these vertices adjacency matrix can be expressed as

Q: Show that p (p(n)) ≤n/2, for n ≥ 2.

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Q: Suppose someone is given the option of having either a guaranteed $20 a 21 % chance at $9, otherwise…

A: To find the expected value of Option 2, we will calculate the weighted average of the possible…

Q: Solve the system -6 -2 =B]. dx 20 6 dt 2 -[:] -2 with x (0) = x2= 8 Give your solution in real form.…

A: The given system is   with initial condition               Let  The characteristic equation…

Q: Find the corresponding linear system near each critical point.

A: For the given system,.To find the corresponding linear system near each of critical points.

Q: H.W Find the Laplace Transform of Find L sin h2tdt [te™ sin tdt 0

A: Here we have to find the laplace of two given f(t).

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE AND DETAILED SOLUTIONS FOR BETTER UNDERSTANDING.…

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Q: 1) Given data 1.6 2 8 4.5 f(x) 2 2 a) Calculate f(2.9) using Newton's interpolating polynomials of…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: If T: P₁ → P₁ is a linear transformation such that T(1 + 5x) = 2 + 2x and T(4+19x) = 1 +2x, then…

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Q: 0 2 10 2 -12 HEMENGED 0 0 0 4 Determine a basis for H which consists of a subset of the given…

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Q: □ x² + y² = 9 2 y = x + 3

A: